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REVIEW 3 major objections 5 minor 137 references

A confederacy of anomalies

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read A personal recollection of the first twenty years of lattice gauge theory claims that the author independently arrived at the lattice action now known as the Wilson action at Christmas 1972, before Wilson's 1974 paper.

desk verdict A credible but uncorroborated personal memoir of early lattice gauge theory; worth preserving, but the Christmas 1972 priority claim rests on memory alone. read the letter →

arxiv 2502.03066 v2 pith:UJ7P4WVK submitted 2025-02-05 hep-lat hep-phhep-thphysics.hist-ph

Jan Smit This is my paper · ORCID
classification hep-lathep-phhep-thphysics.hist-ph PACS 11.15.Ha
keywords latticegaugetheoryfermiondoublingchiralanomalyWilsonactionfermionsstaggeredsymmetryQCD
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This is a personal recollection of roughly the first twenty years of lattice gauge theory, written by a participant. The paper's strongest claim is historical: at Christmas 1972, at a kitchen table in Los Angeles, the author arrived at the lattice action using unitary gauge-group link variables that later became known as the Wilson action. It also claims that during 1973 the author put naive fermions on that lattice, found the eightfold fermion doubling, saw the chiral triangle diagrams vanish, and recognized that the doubling problem and the chiral anomaly were two faces of one phenomenon. These recollections frame the later development of Wilson fermions, staggered fermions, the no-go theorem for chiral fermions on the lattice, and the long quest for a chiral lattice Standard Model. A reader should care because, if the memory is right, a standard piece of the field's origin story is incomplete.

What carries the argument

The load-bearing object is the lattice action with unitary gauge-group link variables, now known as the Wilson action, together with the naive lattice fermion propagator whose spatial momentum function $P_j(k)=\sin(ak_j)/a$ has eight zeros in the Brillouin zone. Those eight zeros are the doublers; the paper uses the Poincaré–Hopf theorem to say that on a momentum-space torus of Euler characteristic zero the indices of the vector field $P_\mu(k)$ must sum to zero, and identifies the index $Q_5$ with the axial charge, so $\sum Q_5=0$ forces anomaly cancellation in the triangle diagrams. A Wilson-type mass term, made gauge invariant through the Higgs field, is what later lifted the doubler masses and produced the flavor-$U(1)$ anomaly.

What would settle it

A contemporaneous document would settle the priority claim: the letter the author's PhD advisor sent in 1983 to the researcher credited with the action, or any 1972-73 notebook, seminar record, or draft of the 1974 thesis. If no such document exists, the Christmas 1972 date and the 1973 calculation rest on testimony alone.

Watch

Extended reading notes

Core claim

The paper sets out to establish that the lattice gauge theory action with unitary gauge-group fields, the object now commonly called the Wilson action, was conceived independently by the author in 1972-73, and that the central difficulties of lattice fermions were identified in his own one-loop calculations before the literature caught up. In his account, the 1973 perturbative calculation gave a fermion propagator $S_F(k)^{-1}=m+i\gamma_0 k_0+\sum_j i\gamma_j P_j(k)$ with $P_j(k)=\sin(ak_j)/a$, producing self-energies a factor 8 too large and vanishing triangle diagrams. The vanishing is later explained by the sum of axial charges $\sum Q_5=0$: the eight species carry axial charges $1,-3,3,-1$ in continuous time (or $1,-4,6,-4,1$ on a Euclidean lattice), so the anomaly cancels exactly, and a Wilson-type mass term $\tilde{r}$ lifts the doubler masses while leaving that anomaly sum zero. The paper thus treats fermion doubling, chiral anomalies, and lattice topology as one story, with the Poincaré–Hopf theorem as the unifying constraint.

Load-bearing premise

The load-bearing premise is the accuracy of the author's memory: the paper gives no contemporaneous notes or letters from 1972-73, and its own Added Note concedes that some relevant proceedings were inaccessible until recently, so every priority and dating claim depends on recollection.

Editorial extensions

If this is right

  • If the priority claim holds, the standard attribution of the lattice action to Wilson alone is incomplete; the same construction was reached independently by the author at Christmas 1972.
  • Doublers are physical particles in the naive lattice theory, not artifacts of a bad regulator: they are unitarily related to the wanted fermion, and in lattice QED they could be pair-produced.
  • A chiral symmetry that is exact on the lattice cannot produce the chiral anomaly in the continuum limit; to get the anomaly one must start with broken chiral symmetry, which is what Wilson fermions do.
  • In the lattice Higgs-fermion models studied with Wilson-Yukawa couplings, removing doublers near the strong-coupling branch turns the remaining fermions into SU(2)$_L$-neutral bound states, so the straightforward lattice version of the Standard Model does not work; the mirror-fermion interpretation gives larger mirror masses.
  • Domain-wall fermions and the later exact chiral symmetry on the lattice opened a route that the early attempts could not, and the paper regards Wilson's original formulation as a valid definition of Euclidean QCD.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial: The historical claim could be checked archivally: the letter the author's PhD advisor sent in 1983, or any 1972-73 notebook, seminar record, or draft of the 1974 thesis, would corroborate or undermine the priority claim.
  • Editorial: If the priority claim is true, the episode shows that the lattice action and the fermion-doubling obstacle were discovered more than once, and that the bottleneck in the early history was not the action itself but the physics of chiral fermions.
  • Editorial: The $\sum Q_5=0$ argument reads like a direct precursor of the published no-go theorem for chiral fermions on the lattice; it suggests the topological understanding was already in the air before the theorem appeared.
  • Editorial: The Wilson-Yukawa phase-diagram work suggests a testable general lesson: any lattice regularization of the Standard Model with fundamental scalars must either keep doublers or lose chirality, unless new ingredients such as domain walls or overlap fermions are introduced.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript is a personal recollection by Jan Smit covering roughly the first twenty years of lattice gauge theory, with emphasis on chiral symmetry and lattice fermions. It recounts his independent arrival at the unitary-link lattice action (now called the Wilson action) at Christmas 1972, his 1973 one-loop calculations exhibiting the fermion-doubling factor 8 and vanishing triangle diagrams, his later work with Karsten on species doubling and the chiral anomaly, the Wilson-Yukawa approach to chiral gauge theories, staggered fermions, and the development of lattice QCD up to the early 1990s. The strongest claim is historical: that Smit independently formulated lattice gauge theory with unitary link variables before Wilson's 1974 paper and recognized the fermion doubling problem in 1973.

Significance. If accepted, the historical claim would revise the standard attribution of the lattice gauge theory action and document an early recognition of the fermion doubling problem. The physics recalled is standard and internally coherent: the eight zeros of P_j(k), the factor-8 vacuum polarization, the vanishing triangle diagrams, and the later Poincaré-Hopf index argument are all consistent with published results, much of which appeared in references [35], [36], [58], and [60]. The narrative also provides a useful first-hand account of the development of Wilson-Yukawa models and the struggle with lattice chiral gauge theories. However, the paper is a memoir, and its central priority claim currently rests on self-reported memory without contemporaneous documentation; no machine-checked proofs, reproducible code, parameter-free derivations, or falsifiable predictions are offered. The significance of the paper therefore depends entirely on the trustworthiness of the author's recollection, which the manuscript itself does not establish.

major comments (3)
  1. [§1 (Prologue)] The central priority claim — "At Christmas 1972 the problem was solved at the kitchen table when I arrived at the lattice action using unitary gauge-group fields (generally known as the Wilson action)" — is supported only by the author's memory. No contemporaneous notebook, preprint, or letter is quoted. The later 1983 Finkelstein letter to Wilson is mentioned but not reproduced or summarized, and the reference list does not include any review by Wilson in which he "mentions" the work as promised. To make this claim archival, either reproduce the relevant documents or explicitly frame the claim as an unverified personal recollection.
  2. [§2 (Back to the lattice)] The exchange with Wilson at Cargèse in 1983 is reported as: "Ask your PhD advisor to send me a description of what you did and I shall mention it in future reviews. So it was done." The phrase "So it was done" asserts that the promised mention occurred, but no such published mention by Wilson is cited in the references. If no published mention exists, the sentence should be revised to reflect that the outcome of the letter is not documented in this manuscript.
  3. [Added Note] The Added Note states that the author had been "unable to access proceedings of the conference mentioned in footnote 10, except very recently" and then supplies details about the Marseille Colloquium. This admission indicates that significant parts of the chronology have been reconstructed from memory. The paper should explicitly distinguish assertions based on documents from assertions based on recollection, and should state the date or source of the "very recent" access so that readers can judge the reliability of the chronology.
minor comments (5)
  1. [§1] There is a typo in the sentence "The fermion part of the Larangian was given by": "Larangian" should be "Lagrangian".
  2. [§1] The phrase "it was a also pleasure attending lectures" is ungrammatical; it should read "it was also a pleasure attending lectures".
  3. [§1] "This led to working on Regge pole theory" is followed by "Backward pion-nucleon scattering was tackled... Comparison with real experimental results turned out give a special exiting thrill" — "exiting" should be "exciting", and "turned out give" should be "turned out to give".
  4. [§1] The text uses "Atiya-Singer index theorem"; the correct spelling is "Atiyah-Singer index theorem".
  5. [Throughout] Several author names contain encoding artifacts, such as "Münster" rendered as "Münster" or "Lüscher" rendered as "Lüscher"; these should be typeset with proper UTF-8 diacritics.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is a historical recollection whose physics claims are standard lattice-fermion results, not derivations from fitted inputs or self-citations.

full rationale

This manuscript makes no new derivational claim and contains no chain in which an output is equivalent to an input by construction. The recounted physics—the eight zeros of P_j(k) = sin(a k_j)/a, the factor-8 self-energies, the vanishing VVA triangle diagrams, Karsten's explanation via summed axial charges, and the Nielsen–Ninomiya context—is standard lattice-fermion content, presented as past work rather than as a prediction fitted from data. The central historical claim, that the author arrived at the unitary-link lattice action at Christmas 1972, rests on self-reported memory and on a 1983 Finkelstein-to-Wilson letter that is described but not reproduced; the Added Note candidly explains that the author had been unable to access the 1974 Marseille proceedings until recently. That is an evidentiary limitation, not circularity: no quantity is defined in terms of its own conclusion, no fitted parameter is renamed as a prediction, and no load-bearing argument is justified solely by self-citation. Citations to the author's own papers document chronology and are checkable against the published literature, so they serve as independent support rather than a circular chain. The correct finding is therefore no significant circularity.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

No free parameters, no new physical axioms, and no invented entities are introduced. The paper is purely a historical account.

assumptions (2)
  • domain assumption The author's personal recollections of events and conversations are accurate.
    The entire memoir is based on memory; no external verification is provided for many specific claims, such as the date and place of the invention.
  • domain assumption The physics calculations recalled (factor 8, vanishing triangle, etc.) are correctly remembered.
    The calculations are standard but presented from memory without full derivations in this paper.

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Cite this review

Pith. "Pith review of A confederacy of anomalies." pith.science (2026). https://pith.science/paper/UJ7P4WVK

@misc{pith2026250203066,
  author       = {Pith},
  title        = {Pith review of: A confederacy of anomalies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UJ7P4WVK}},
  note         = {Machine review of arXiv:2502.03066}
}
read the original abstract

A personal recollection of early years in lattice gauge theory with a bias towards chiral symmetry and lattice fermions.

Figures

Figures reproduced from arXiv: 2502.03066 by the authors.

Figure 1
Figure 1. Momentum functions Pj (k) of an N = 64 lattice versus akj in the interval (−π, π]. Bottom to top at akj = 2: Pj (k) = sin(akj )/a (“naive”), 2 sin(akj/2)/a (“modified”), kj (“SLAC”). In the right plot, the left-plot modes in (−π, 0) have been shifted by 2π: 0 ≤ akj < 2π. Lattice units a = 1. The j-component of the three-vector P⃗ (k) is illustrated in the left plot of [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Reference graph

Works this paper leans on

137 extracted references · 75 canonical work pages

  1. [35]

    Karsten and J

    L.H. Karsten and J. Smit, Axial Symmetry in Lattice Theories , Nucl. Phys. B 144 (1978) 536

    1978

  2. [36]

    Karsten and J

    L.H. Karsten and J. Smit, The Vacuum Polarization With SLAC Lattice Fermions, Phys. Lett. B 85 (1979) 100

    1979

  3. [58]

    Karsten and J

    L.H. Karsten and J. Smit, Lattice Fermions: Species Doubling, Chiral Invariance, and the Triangle Anomaly , Nucl. Phys. B 183 (1981) 103

    work page 1981

  4. [60]

    Karsten, Lattice Fermions in Euclidean Space-time, Phys

    L.H. Karsten, Lattice Fermions in Euclidean Space-time, Phys. Lett. B 104 (1981) 315

    work page 1981

  5. [1]

    Veltman, Perturbation theory of massive Yang-Mills fields , Nucl

    M.J.G. Veltman, Perturbation theory of massive Yang-Mills fields , Nucl. Phys. B 7 (1968) 637

    1968

  6. [2]

    Weinberg, A Model of Leptons , Phys

    S. Weinberg, A Model of Leptons , Phys. Rev. Lett. 19 (1967) 1264

    1967

  7. [3]

    Wilson, Nonlagrangian models of current algebra , Phys

    K.G. Wilson, Nonlagrangian models of current algebra , Phys. Rev. 179 (1969) 1499

    1969

  8. [4]

    Wilson, Operator Product Expansions and Anomalous Dimensions in the Thirring Model, Phys

    K.G. Wilson, Operator Product Expansions and Anomalous Dimensions in the Thirring Model, Phys. Rev. D 2 (170) 1473

Show all 137 references
  1. [5]

    Wilson, The Renormalization Group and Strong Interactions , Phys

    K.G. Wilson, The Renormalization Group and Strong Interactions , Phys. Rev. D 3 (1971) 1818

    1971

  2. [6]

    Wilson, Renormalization group and critical phenomena I

    K.G. Wilson, Renormalization group and critical phenomena I. Renormalization group and the Kadanoff scaling picture , Phys. Rev. B 4 (1971) 3174

    1971

  3. [7]

    Wilson, Renormalization group and critical phenomena II

    K.G. Wilson, Renormalization group and critical phenomena II. Phase space cell analysis of critical behavior , Phys. Rev. B 4 (1971) 3184

    1971

  4. [8]

    Smit, Conformal Invariance and Indefinite Metric , ITF A-71-2200 (1971)

    J. Smit, Conformal Invariance and Indefinite Metric , ITF A-71-2200 (1971)

    1971

  5. [9]

    Wiegel, The Interacting Bose Fluid: Path Integral Representations and Renormalization Group Approach, NATO Sci

    F.W. Wiegel, The Interacting Bose Fluid: Path Integral Representations and Renormalization Group Approach, NATO Sci. Ser. B 34 (1978) 419

    1978

  6. [10]

    Boulware, Renormalizeability of massive non-abelian gauge fields - a functional integral approach, Annals Phys

    D.G. Boulware, Renormalizeability of massive non-abelian gauge fields - a functional integral approach, Annals Phys. 56 (1970) 140

    1970

  7. [11]

    Rzewuski, Field Theory, Iliffe Books, London (1969)

    J. Rzewuski, Field Theory, Iliffe Books, London (1969)

    1969

  8. [12]

    Adler, Axial vector vertex in spinor electrodynamics , Phys

    S.L. Adler, Axial vector vertex in spinor electrodynamics , Phys. Rev. 177 (1969) 2426

    1969

  9. [13]

    Bell and R

    J.S. Bell and R. Jackiw, A PCAC puzzle: π0 → γγ in the σ model, Nuovo Cim. A 60 (1969) 47

    1969

  10. [14]

    Bouchiat, J

    C. Bouchiat, J. Iliopoulos and P. Meyer, An Anomaly Free Version of Weinberg’s Model, Phys. Lett. B 38 (1972) 519

    1972

  11. [15]

    Gross and R

    D.J. Gross and R. Jackiw, Effect of anomalies on quasirenormalizable theories , Phys. Rev. D 6 (1972) 477

    1972

  12. [16]

    Adler, Perturbation Theory Anomalies, Brandeis University Summer Institute in Theoretical Physics, MIT press (1970)

    S.L. Adler, Perturbation Theory Anomalies, Brandeis University Summer Institute in Theoretical Physics, MIT press (1970)

    1970

  13. [17]

    Schwinger, Particles and Sources , Addison-Wesley (1969)

    J. Schwinger, Particles and Sources , Addison-Wesley (1969)

    1969

  14. [18]

    Schwinger, Particles, Sources, and Fields

    J. Schwinger, Particles, Sources, and Fields. Volume I , Addison-Wesley (1970)

    1970

  15. [19]

    Schwinger, Particles, Sources and Fields

    J.S. Schwinger, Particles, Sources and Fields. Volume II , Addison-Wesley (1973)

    1973

  16. [20]

    Finkelstein and J

    R.J. Finkelstein and J. Smit, Massive gauge field in source theory. 2. , Annals Phys. 88 (1974) 157. 14

    1974

  17. [21]

    Cornwall and R.E

    J.M. Cornwall and R.E. Norton, Spontaneous Symmetry Breaking Without Scalar Mesons, Phys. Rev. D 8 (1973) 3338

    1973

  18. [22]

    Smit, On the Possibility That Massless Yang-Mills Fields Generate Massive Vector Particles, Phys

    J. Smit, On the Possibility That Massless Yang-Mills Fields Generate Massive Vector Particles, Phys. Rev. D 10 (1974) 2473

    1974

  19. [23]

    Wilson and J.B

    K.G. Wilson and J.B. Kogut, The Renormalization group and the epsilon expansion, Phys. Rept. 12 (1974) 75

    1974

  20. [24]

    Wilson, Confinement of Quarks , Phys

    K.G. Wilson, Confinement of Quarks , Phys. Rev. D 10 (1974) 2445

    1974

  21. [25]

    Drell, M

    S.D. Drell, M. Weinstein and S. Yankielowicz, Strong Coupling Field Theories II, Fermions and Gauge Fields on a Lattice , Phys. Rev. D 14 (1976) 1627

    1976

  22. [26]

    Wilson, Quarks and Strings on a Lattice , in 13th International School of Subnuclear Physics: New Phenomena in Subnuclear Physics , 11, 1975

    K.G. Wilson, Quarks and Strings on a Lattice , in 13th International School of Subnuclear Physics: New Phenomena in Subnuclear Physics , 11, 1975

    1975

  23. [27]

    Kogut and L

    J.B. Kogut and L. Susskind, Hamiltonian Formulation of Wilson ’s Lattice Gauge Theories, Phys. Rev. D 11 (1975) 395

    1975

  24. [28]

    Susskind, Lattice Fermions, Phys

    L. Susskind, Lattice Fermions, Phys. Rev. D 16 (1977) 3031

    1977

  25. [29]

    Balian, J.M

    R. Balian, J.M. Drouffe and C. Itzykson, Gauge Fields on a Lattice. III. Strong Coupling Expansions and Transition Points , Phys. Rev. D 11 (1975) 2104

    1975

  26. [30]

    Cornell-Oxford-Tel A viv-Yeshivacollaboration, Strong Coupling Calculations of the Hadron Spectrum of Quantum Chromodynamics , Phys. Rev. D 15 (1977) 1111

    1977

  27. [31]

    Sharatchandra, The Continuum Limit of Lattice Gauge Theories in the Context of Renormalized Perturbation Theory , Phys

    H.S. Sharatchandra, The Continuum Limit of Lattice Gauge Theories in the Context of Renormalized Perturbation Theory , Phys. Rev. D 18 (1978) 2042

    1978

  28. [32]

    Baaquie, Gauge Fixing and Mass Renormalization in the Lattice Gauge Theory, Phys

    B.E. Baaquie, Gauge Fixing and Mass Renormalization in the Lattice Gauge Theory, Phys. Rev. D 16 (1977) 2612

    1977

  29. [33]

    Creutz, Gauge Fixing, the Transfer Matrix, and Confinement on a Lattice , Phys

    M. Creutz, Gauge Fixing, the Transfer Matrix, and Confinement on a Lattice , Phys. Rev. D 15 (1977) 1128

    1977

  30. [34]

    Luscher, Construction of a Selfadjoint, Strictly Positive Transfer Matrix for Euclidean Lattice Gauge Theories , Commun

    M. Luscher, Construction of a Selfadjoint, Strictly Positive Transfer Matrix for Euclidean Lattice Gauge Theories , Commun. Math. Phys. 54 (1977) 283

    1977

  31. [37]

    Shigemitsu, Spectrum Calculations in Lattice Gauge Theory Using Wilson ’s Fermion Method, Phys

    J. Shigemitsu, Spectrum Calculations in Lattice Gauge Theory Using Wilson ’s Fermion Method, Phys. Rev. D 18 (1978) 1709

    1978

  32. [38]

    Greensite, Large Scale Vacuum Structure and New Calculational Techniques in Lattice SU(N ) Gauge Theory , Nucl

    J.P. Greensite, Large Scale Vacuum Structure and New Calculational Techniques in Lattice SU(N ) Gauge Theory , Nucl. Phys. B 166 (1980) 113

    1980

  33. [39]

    Savit, Duality in Field Theory and Statistical Systems , Rev

    R. Savit, Duality in Field Theory and Statistical Systems , Rev. Mod. Phys. 52 (1980) 453

    1980

  34. [40]

    Banks, R

    T. Banks, R. Myerson and J.B. Kogut, Phase Transitions in Abelian Lattice Gauge Theories, Nucl. Phys. B 129 (1977) 493

    1977

  35. [41]

    Fradkin and S.H

    E.H. Fradkin and S.H. Shenker, Phase Diagrams of Lattice Gauge Theories with Higgs Fields , Phys. Rev. D 19 (1979) 3682

    1979

  36. [42]

    Mack and V.B

    G. Mack and V.B. Petkova, Sufficient Condition for Confinement of Static Quarks by a Vortex Condensation Mechanism , Annals Phys. 125 (1980) 117

    1980

  37. [43]

    Munster, On the Characterization of the Higgs Phase in Lattice Gauge Theories, Z

    G. Munster, On the Characterization of the Higgs Phase in Lattice Gauge Theories, Z. Phys. C 6 (1980) 175

    1980

  38. [44]

    Wilson, Monte Carlo Calculations for the Lattice Gauge Theory , NATO Sci

    K.G. Wilson, Monte Carlo Calculations for the Lattice Gauge Theory , NATO Sci. Ser. B 59 (1980) 363. 15

    1980

  39. [45]

    Kogut, R.B

    J.B. Kogut, R.B. Pearson and J. Shigemitsu, The QCD beta Function at Intermediate and Strong Coupling , Phys. Rev. Lett. 43 (1979) 484

    1979

  40. [46]

    Creutz, L

    M. Creutz, L. Jacobs and C. Rebbi, Monte Carlo Study of Abelian Lattice Gauge Theories, Phys. Rev. D 20 (1979) 1915

    1979

  41. [47]

    Creutz, Solving Quantized SU(2) Gauge Theory , Print-79-0919 (BNL) (1979)

    M. Creutz, Solving Quantized SU(2) Gauge Theory , Print-79-0919 (BNL) (1979)

    1979

  42. [48]

    Creutz, Monte Carlo Study of Quantized SU(2) Gauge Theory , Phys

    M. Creutz, Monte Carlo Study of Quantized SU(2) Gauge Theory , Phys. Rev. D 21 (1980) 2308

    1980

  43. [49]

    Creutz, Asymptotic Freedom Scales, Phys

    M. Creutz, Asymptotic Freedom Scales, Phys. Rev. Lett. 45 (1980) 313

    1980

  44. [50]

    Karsten, The Lattice Fermion Problem and Weak Coupling Perturbation Theory, NATO Sci

    L.H. Karsten, The Lattice Fermion Problem and Weak Coupling Perturbation Theory, NATO Sci. Ser. B 55 (1980) 235

    1980

  45. [51]

    Banks and A

    T. Banks and A. Casher, Chiral Symmetry Breaking in Confining Theories , Nucl. Phys. B 169 (1980) 103

    1980

  46. [52]

    Kawamoto, Towards the Phase Structure of Euclidean Lattice Gauge Theories with Fermions, Nucl

    N. Kawamoto, Towards the Phase Structure of Euclidean Lattice Gauge Theories with Fermions, Nucl. Phys. B 190 (1981) 617

    1981

  47. [53]

    Smit, Chiral Symmetry Breaking in QCD: Mesons as Spin Waves , Nucl

    J. Smit, Chiral Symmetry Breaking in QCD: Mesons as Spin Waves , Nucl. Phys. B 175 (1980) 307

    1980

  48. [54]

    Greensite and J

    J. Greensite and J. Primack, Pions as Spin Waves: Chiral Symmetry Breaking in Lattice Gauge Theory , Nucl. Phys. B 180 (1981) 170

    1981

  49. [55]

    Svetitsky, S.D

    B. Svetitsky, S.D. Drell, H.R. Quinn and M. Weinstein, Dynamical Breaking of Chiral Symmetry in Lattice Gauge Theories , Phys. Rev. D 22 (1980) 490

    1980

  50. [56]

    Weinstein, S.D

    M. Weinstein, S.D. Drell, H.R. Quinn and B. Svetitsky, Approximate Dynamical Symmetry in Lattice Quantum Chromodynamics , Phys. Rev. D 22 (1980) 1190

    1980

  51. [57]

    Blairon, R

    J.M. Blairon, R. Brout, F. Englert and J. Greensite, Chiral Symmetry Breaking in the Action Formulation of Lattice Gauge Theory , Nucl. Phys. B 180 (1981) 439

    1981

  52. [59]

    Groot, J

    R. Groot, J. Hoek and J. Smit, Normalization of Currents in Lattice QCD , Nucl. Phys. B 237 (1984) 111

    1984

  53. [61]

    Nielsen and M

    H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. 1. Proof by Homotopy Theory, Nucl. Phys. B 185 (1981) 20

    1981

  54. [62]

    Nielsen and M

    H.B. Nielsen and M. Ninomiya, Absence of Neutrinos on a Lattice. 2. Intuitive Topological Proof, Nucl. Phys. B 193 (1981) 173

    1981

  55. [63]

    Nielsen and M

    H.B. Nielsen and M. Ninomiya, No Go Theorem for Regularizing Chiral Fermions, Phys. Lett. B 105 (1981) 219

    1981

  56. [64]

    Witten, Current Algebra Theorems for the U(1) Goldstone Boson , Nucl

    E. Witten, Current Algebra Theorems for the U(1) Goldstone Boson , Nucl. Phys. B 156 (1979) 269

    1979

  57. [65]

    Veneziano, U(1) Without Instantons , Nucl

    G. Veneziano, U(1) Without Instantons , Nucl. Phys. B 159 (1979) 213

    1979

  58. [66]

    Di Vecchia, K

    P. Di Vecchia, K. Fabricius, G.C. Rossi and G. Veneziano, Preliminary Evidence for U(1)-A Breaking in QCD from Lattice Calculations , Nucl. Phys. B 192 (1981) 392

    1981

  59. [67]

    Luscher, Topology of Lattice Gauge Fields , Commun

    M. Luscher, Topology of Lattice Gauge Fields , Commun. Math. Phys. 85 (1982) 39. 16

    1982

  60. [68]

    Kawamoto and J

    N. Kawamoto and J. Smit, Effective Lagrangian and Dynamical Symmetry Breaking in Strongly Coupled Lattice QCD , Nucl. Phys. B 192 (1981) 100

    1981

  61. [69]

    Kluberg-Stern, A

    H. Kluberg-Stern, A. Morel, O. Napoly and B. Petersson, Spontaneous Chiral Symmetry Breaking for a U(N) Gauge Theory on a Lattice , Nucl. Phys. B 190 (1981) 504

    1981

  62. [70]

    Alessandrini, V

    V. Alessandrini, V. Hakim and A. Krzywicki, Chiral Symmetry in the Mean Field Approach to Large N Lattice QCD, Nucl. Phys. B 205 (1982) 253

    1982

  63. [71]

    J. Hoek, N. Kawamoto and J. Smit, Baryons in the Effective Lagrangian of Strongly Coupled Lattice QCD , Nucl. Phys. B 199 (1982) 495

    1982

  64. [72]

    Hoek, Strong Coupling Expansion of the Generating Functional for Gauge Systems on a Lattice With Arbitrary Sources , J

    J. Hoek, Strong Coupling Expansion of the Generating Functional for Gauge Systems on a Lattice With Arbitrary Sources , J. Comput. Phys. 49 (1983) 265

    1983

  65. [73]

    Hoek, Strong Coupling Expansion Of The SU(3) AND U(3) Effective Actions, J

    J. Hoek, Strong Coupling Expansion Of The SU(3) AND U(3) Effective Actions, J. Comput. Phys. 54 (1984) 245

    1984

  66. [74]

    Hoek and J

    J. Hoek and J. Smit, On the 1/ g2 Corrections to Hadron Masses , Nucl. Phys. B 263 (1986) 129

    1986

  67. [75]

    Munster, High Temperature Expansions for the Free Energy of Vortices, Respectively the String Tension in Lattice Gauge Theories , Nucl

    G. Munster, High Temperature Expansions for the Free Energy of Vortices, Respectively the String Tension in Lattice Gauge Theories , Nucl. Phys. B 180 (1981) 23

    1981

  68. [76]

    Munster, Strong Coupling Expansions for the Mass Gap in Lattice Gauge Theories, Nucl

    G. Munster, Strong Coupling Expansions for the Mass Gap in Lattice Gauge Theories, Nucl. Phys. B 190 (1981) 439

    1981

  69. [77]

    Munster, Physical Strong Coupling Expansion Parameters and Glueball Mass Ratios, Phys

    G. Munster, Physical Strong Coupling Expansion Parameters and Glueball Mass Ratios, Phys. Lett. B 121 (1983) 53

    1983

  70. [78]

    Hoek, Effective Action Calculation in Lattice QCD , Ph.D

    J. Hoek, Effective Action Calculation in Lattice QCD , Ph.D. thesis, Amsterdam U., 1983

    1983

  71. [79]

    Greensite, T.H

    J. Greensite, T.H. Hansson, N.D. Hari Dass and P.G. Lauwers, Calculations in the Weak and Crossover Regions of SU(2) Lattice Gauge Theory , Phys. Lett. B 105 (1981) 201

    1981

  72. [80]

    Hari Dass and P.G

    N.D. Hari Dass and P.G. Lauwers, Some Approximate Calculations in SU(2) Lattice Mean Field Theory , Nucl. Phys. B 210 (1982) 388

    1982

  73. [81]

    Kogut, A Review of the Lattice Gauge Theory Approach to Quantum Chromodynamics, Rev

    J.B. Kogut, A Review of the Lattice Gauge Theory Approach to Quantum Chromodynamics, Rev. Mod. Phys. 55 (1983) 775

    1983

  74. [82]

    Creutz, L

    M. Creutz, L. Jacobs and C. Rebbi, Monte Carlo Computations in Lattice Gauge Theories, Phys. Rept. 95 (1983) 201

    1983

  75. [83]

    Sharatchandra, H.J

    H.S. Sharatchandra, H.J. Thun and P. Weisz, Susskind Fermions on a Euclidean Lattice, Nucl. Phys. B 192 (1981) 205

    1981

  76. [84]

    Rabin, Perturbation Theory for SLAC Lattice Fermions , Phys

    J.M. Rabin, Perturbation Theory for SLAC Lattice Fermions , Phys. Rev. D 24 (1981) 3218

    1981

  77. [85]

    Rabin, Homology Theory of Lattice Fermion Doubling , Nucl

    J.M. Rabin, Homology Theory of Lattice Fermion Doubling , Nucl. Phys. B 201 (1982) 315

    1982

  78. [86]

    Becher, Dirac Fermions on the Lattice: A Local Approach Without Spectrum Degeneracy, Phys

    P. Becher, Dirac Fermions on the Lattice: A Local Approach Without Spectrum Degeneracy, Phys. Lett. B 104 (1981) 221

    1981

  79. [87]

    Becher and H

    P. Becher and H. Joos, The Dirac-K¨ ahler Equation and Fermions on the Lattice, Z. Phys. C 15 (1982) 343

    1982

  80. [88]

    Gliozzi, Spinor Algebra of the One Component Lattice Fermions , Nucl

    F. Gliozzi, Spinor Algebra of the One Component Lattice Fermions , Nucl. Phys. B 204 (1982) 419

    1982

  81. [89]

    Kluberg-Stern, A

    H. Kluberg-Stern, A. Morel, O. Napoly and B. Petersson, Flavors of Lagrangian Susskind Fermions, Nucl. Phys. B 220 (1983) 447. 17

    1983

  82. [90]

    Jolicoeur, H

    T. Jolicoeur, H. Kluberg-Stern, M. Lev, A. Morel and B. Petersson, The Strong Coupling Expansion of Lattice Gauge Theories With Susskind Fermions , Nucl. Phys. B 235 (1984) 455

    1984

  83. [91]

    van den Doel and J

    C. van den Doel and J. Smit, Dynamical Symmetry Breaking in Two Flavor SU(N ) and SO( N ) Lattice Gauge Theories , Nucl. Phys. B 228 (1983) 122

    1983

  84. [92]

    Ginsparg and K.G

    P.H. Ginsparg and K.G. Wilson, A Remnant of Chiral Symmetry on the Lattice, Phys. Rev. D 25 (1982) 2649

    1982

  85. [93]

    Banks and V

    T. Banks and V. Kaplunovsky, Composite Massless Fermions in Strongly Coupled Lattice Gauge Theories , Nucl. Phys. B 192 (1981) 270

    1981

  86. [94]

    Banks and A

    T. Banks and A. Zaks, On the Phase Structure of Vector-Like Gauge Theories with Massless Fermions , Nucl. Phys. B 196 (1982) 189

    1982

  87. [95]

    Wilson, Monte Carlo Renormalization Group and the Three-Dimensional Ising Model, NATO Sci

    K.G. Wilson, Monte Carlo Renormalization Group and the Three-Dimensional Ising Model, NATO Sci. Ser. B 115 (1984) 589

    1984

  88. [96]

    Golterman and J

    M.F.L. Golterman and J. Smit, Relation Between QCD Parameters on the Lattice and in the Continuum , Phys. Lett. B 140 (1984) 392

    1984

  89. [97]

    Golterman and J

    M.F.L. Golterman and J. Smit, Selfenergy and Flavor Interpretation of Staggered Fermions, Nucl. Phys. B 245 (1984) 61

    1984

  90. [98]

    Golterman and J

    M.F.L. Golterman and J. Smit, Lattice Baryons With Staggered Fermions , Nucl. Phys. B 255 (1985) 328

    1985

  91. [99]

    Golterman, Staggered Mesons, Nucl

    M.F.L. Golterman, Staggered Mesons, Nucl. Phys. B 273 (1986) 663

    1986

  92. [100]

    Golterman, Irreducible Representations of the Staggered Fermion Symmetry Group, Nucl

    M.F.L. Golterman, Irreducible Representations of the Staggered Fermion Symmetry Group, Nucl. Phys. B 278 (1986) 417

    1986

  93. [101]

    Daniel and T.D

    D. Daniel and T.D. Kieu, On the Flavor Interpretations of Staggered Fermions , Phys. Lett. B 175 (1986) 73

    1986

  94. [102]

    Kilcup and S.R

    G.W. Kilcup and S.R. Sharpe, A Tool Kit for Staggered Fermions , Nucl. Phys. B 283 (1987) 493

    1987

  95. [103]

    Coste, C

    A. Coste, C. Korthals Altes and O. Napoly, Calculation of the Nonabelian Chiral Anomaly on the Lattice , Nucl. Phys. B 289 (1987) 645

    1987

  96. [104]

    Konig, K.H

    A. Konig, K.H. Mutter, K. Schilling and J. Smit, Large Distance Propagators for Hadrons on a 56 X 16**3 Lattice , Phys. Lett. B 157 (1985) 421

    1985

  97. [105]

    Bowler, F

    K.C. Bowler, F. Gutbrod, P. Hasenfratz, U.M. Heller, F. Karsch, R.D. Kenway et al., The Beta Function and Potential at Beta = 6 and 6.3 in S(3) Gauge Theory, Phys. Lett. B 163 (1985) 367

    1985

  98. [106]

    Luscher, Symmetry Breaking Aspects of the Roughening Transition in Gauge Theories, Nucl

    M. Luscher, Symmetry Breaking Aspects of the Roughening Transition in Gauge Theories, Nucl. Phys. B 180 (1981) 317

    1981

  99. [107]

    Kogut and D.K

    J.B. Kogut and D.K. Sinclair, On the Analyticity of the Off-axis String Tension and the Restoration of Rotational Symmetry in Lattice Systems , Phys. Rev. D 24 (1981) 1610

    1981

  100. [108]

    Luscher, Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories

    M. Luscher, Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories. 2. Scattering States , Commun. Math. Phys. 105 (1986) 153

    1986

  101. [109]

    Luscher, Signatures of unstable particles in finite volume , Nucl

    M. Luscher, Signatures of unstable particles in finite volume , Nucl. Phys. B 364 (1991) 237

    1991

  102. [110]

    Smit and J.C

    J. Smit and J.C. Vink, Neutral Pseudoscalar Masses in Lattice QCD , Nucl. Phys. B 284 (1987) 234

    1987

  103. [111]

    Smit and J.C

    J. Smit and J.C. Vink, Renormalized Ward-takahashi Relations and Topological Susceptibility With Staggered Fermions, Nucl. Phys. B 298 (1988) 557. 18

    1988

  104. [112]

    Smit and J.C

    J. Smit and J.C. Vink, Remnants of the Index Theorem on the Lattice , Nucl. Phys. B 286 (1987) 485

    1987

  105. [113]

    J. Hoek, M. Teper and J. Waterhouse, Topological Fluctuations and Susceptibility in SU(3) Lattice Gauge Theory , Nucl. Phys. B 288 (1987) 589

    1987

  106. [114]

    Berg, Dislocations and Topological Background in the Lattice O(3) σ Model, Phys

    B. Berg, Dislocations and Topological Background in the Lattice O(3) σ Model, Phys. Lett. B 104 (1981) 475

    1981

  107. [115]

    Fucito, E

    F. Fucito, E. Marinari, G. Parisi and C. Rebbi, A Proposal for Monte Carlo Simulations of Fermionic Systems , Nucl. Phys. B 180 (1981) 369

    1981

  108. [116]

    Swift, The Electroweak Theory on the Lattice , Phys

    P.V.D. Swift, The Electroweak Theory on the Lattice , Phys. Lett. B 145 (1984) 256

    1984

  109. [117]

    Smit, Fermions on a Lattice , Acta Phys

    J. Smit, Fermions on a Lattice , Acta Phys. Polon. B 17 (1986) 531

    1986

  110. [118]

    D’Hoker and E

    E. D’Hoker and E. Farhi, Decoupling a Fermion in the Standard Electroweak Theory, Nucl. Phys. B 248 (1984) 77

    1984

  111. [119]

    Hands and D.B

    S.J. Hands and D.B. Carpenter, Lattice σ Model and Fermion Doubling , Nucl. Phys. B 266 (1986) 285

    1986

  112. [120]

    Luscher and P

    M. Luscher and P. Weisz, Scaling Laws and Triviality Bounds in the Lattice phi**4 Theory. 1. One Component Model in the Symmetric Phase , Nucl. Phys. B 290 (1987) 25

    1987

  113. [121]

    Luscher and P

    M. Luscher and P. Weisz, Is there a strong interaction sector in the Standard Lattice Higgs Model?, Phys. Lett. B212 (1988) 472

    1988

  114. [122]

    Bock, A.K

    W. Bock, A.K. De, K. Jansen, J. Jersak, T. Neuhaus and J. Smit, Phase Diagram of a Lattice SU(2) X SU(2) Scalar Fermion Model With Naive and Wilson Fermions, Nucl. Phys. B 344 (1990) 207

    1990

  115. [123]

    Bock, A.K

    W. Bock, A.K. De, C. Frick, K. Jansen and T. Trappenberg, Search for an upper bound of the renormalized Yukawa coupling in a lattice fermion Higgs model, Nucl. Phys. B 371 (1992) 683

    1992

  116. [124]

    Bock, A.K

    W. Bock, A.K. De and J. Smit, Fermion masses at strong Wilson-Yukawa coupling in the symmetric phase , Nucl. Phys. B 388 (1992) 243

    1992

  117. [125]

    Golterman, D.N

    M.F.L. Golterman, D.N. Petcher and J. Smit, Fermion interactions in models with strong Wilson-Yukawa couplings , Nucl. Phys. B 370 (1992) 51

    1992

  118. [126]

    Aoki, I.-H

    S. Aoki, I.-H. Lee, J. Shigemitsu and R.E. Shrock, Fermions in the Hypercharge Sector of the Standard Lattice Electroweak Theory: Global Limit , Phys. Lett. B 243 (1990) 403

    1990

  119. [127]

    Aoki, I.-H

    S. Aoki, I.-H. Lee and R.E. Shrock, Decoupling of doubler modes and tuning of fermion masses in the SU(2) x U(1)-Y lattice electroweak theory , Phys. Rev. D 45 (1992) 13

    1992

  120. [128]

    Frick, T

    C. Frick, T. Trappenberg, L. Lin, G. Munster, M. Plagge, I. Montvay et al., Numerical simulation of heavy fermions in an SU(2)-L x SU(2)-R symmetric Yukawa model, Nucl. Phys. B 397 (1993) 431 [ hep-lat/9207021]

    1993 arXiv

  121. [129]

    Borrelli, L

    A. Borrelli, L. Maiani, R. Sisto, G.C. Rossi and M. Testa, Neutrinos on the Lattice: The Regularization of a Chiral Gauge Theory , Nucl. Phys. B 333 (1990) 335

    1990

  122. [130]

    W. Bock, J. Smit and J.C. Vink, Nongauge fixing approach to chiral gauge theories using staggered fermions , Nucl. Phys. B 416 (1994) 645 [hep-lat/9308009]

    1994 arXiv

  123. [131]

    Banks and A

    T. Banks and A. Dabholkar, Decoupling a fermion whose mass comes from a Yukawa coupling: Nonperturbative considerations, Phys. Rev. D 46 (1992) 4016 [hep-lat/9204017]. 19

    1992 arXiv

  124. [132]

    Kaplan, A Method for simulating chiral fermions on the lattice , Phys

    D.B. Kaplan, A Method for simulating chiral fermions on the lattice , Phys. Lett. B 288 (1992) 342 [ hep-lat/9206013]

    1992 arXiv

  125. [133]

    Kaplan, Chiral fermions on the lattice , Nucl

    D.B. Kaplan, Chiral fermions on the lattice , Nucl. Phys. B Proc. Suppl. 30 (1993) 597

    1993

  126. [134]

    Luscher, Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation, Phys

    M. Luscher, Exact chiral symmetry on the lattice and the Ginsparg-Wilson relation, Phys. Lett. B 428 (1998) 342 [ hep-lat/9802011]

    1998 arXiv

  127. [135]

    Hamber, E

    H.W. Hamber, E. Marinari, G. Parisi and C. Rebbi, Numerical Simulations of Quantum Chromodynamics, Phys. Lett. B 124 (1983) 99

    1983

  128. [136]

    Kronfeld, Lattice Gauge Theory with Staggered Fermions: How, Where, and Why (Not) , PoS LA TTICE 2007(2007) 016 [ 0711.0699]

    A.S. Kronfeld, Lattice Gauge Theory with Staggered Fermions: How, Where, and Why (Not) , PoS LA TTICE 2007(2007) 016 [ 0711.0699]

    2007 arXiv

  129. [138]

    Korthals Altes, Yang-Mills Fields on a Lattice and Dual Amplitudes , in Marseille Colloquium on Lagrangian Field Theory , 1974, https://www.osti.gov/biblio/4092791

    C.P. Korthals Altes, Yang-Mills Fields on a Lattice and Dual Amplitudes , in Marseille Colloquium on Lagrangian Field Theory , 1974, https://www.osti.gov/biblio/4092791. 20

    1974

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