Coulomb Gauge QCD, Confinement, and the Constituent Representation

Adam P. Szczepaniak (U. Indiana); Eric S. Swanson (U. Pittsburgh)

REVIEW

Coulomb Gauge QCD, Confinement, and the Constituent Representation

Adam P. Szczepaniak (U. Indiana), Eric S. Swanson (U. Pittsburgh)

High Energy Physics - Phenomenology · Submitted 7 Jul 2001 · 35 references

Pith's verdict: A serious, honest coupled-gap-equation calculation in Coulomb-gauge QCD whose near-linear potential is real but sits on a chosen boundary condition and an uncontrolled truncation.

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arXiv IDhep-ph/0107078 (version 1)

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CitationAdam P. Szczepaniak (U. Indiana), Eric S. Swanson (U. Pittsburgh). "Coulomb Gauge QCD, Confinement, and the Constituent Representation." arXiv:hep-ph/0107078 (2001). https://pith.science/paper/ZV2VLVE5

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Editor's note

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Worth your time, with caveats. The core of this paper is a self-consistent set of coupled equations in Coulomb-gauge QCD for three things at once: the VEV of the Faddeev-Popov operator d(k), the instantaneous Coulomb kernel f(k), and the gluon gap function omega(k). That coupling is the new bit relative to Swift [21] and Zwanziger [6,7], and they actually solve it — approximate analytic solution, then a full numerical one, with a grid-refinement stability check (Fig. 7) that I found convincing. At a critical coupling the effective potential comes out nearly linear (V ~ k^-1.93, Eq. 92), and the static potential they Fourier-transform lands close to the lattice Wilson-loop result (Fig. 10). The conceptual payoff is real too: the observation that confinement here is the time component of a vector, which kills the old scalar-confinement problem of antibound baryons, and the sketch in Sec. V.C of how the 3P0 decay vertex falls out of K(1) times Hqg. Those are good ideas, cleanly argued. The abstract's 'agree remarkably well with lattice computations' [abstract:s2] is doing more work than the body supports — the static potential agrees; the gap function omega(k) does not, and they say so in Sec. IV.B. That's an overstatement in the abstract, not in the physics. The two soft spots that matter: the critical coupling d(mg)=dc is not derived, it is selected by requiring the Gribov-Zwanziger IR singularity (Sec. IV.B), and f(mg) and mg are fitted to lattice. They are upfront about both. The stress-test concern about the truncation is fair but partly acknowledged: at d ~ 3.5 the nominal expansion parameter is O(1), the O(d4) check (Fig. 9) omits the FP-determinant pieces VA and VB, and the universality of the critical behavior is asserted in Sec. III.D rather than shown. That is the load-bearing worry, and it is the one thing I would push hardest on in review. But the near-linear shape is not simply dialed in — it comes out of the coupled system given the boundary condition — so this is a truncation-control question, not a circularity. Send it out. The Coulomb-gauge and Gribov-Zwanziger crowd will get real value from the explicit equations and the numerical solution, and the constituent-quark-model phenomenology in Sec. V is worth arguing with.

Referee report

Significance

If it holds, this is a valuable result: a continuum, first-principles derivation that ties confinement and the constituent quark picture to a single self-consistent calculation, with falsifiable consequences (Casimir scaling, vector rather than scalar confinement, and a 3P0-like decay vertex arising from K(1) times Hqg). Credit is due for the explicit derivation of the coupled gap equations, for the numerical stability check against grid size (Fig. 7), for the unusually honest statement of the truncations employed, and for the direct comparison to lattice static-potential data. The paper also makes a genuine conceptual contribution by separating instantaneous from transverse degrees of freedom, which removes a longstanding ambiguity in the constituent quark model between one-gluon exchange and the linear potential.

Major objections (3)

[Sec. IV.B, Eq. (111)] The confinement result is conditional on the choice d(mu)=dc, and this should be stated as such in the abstract and introduction, not only in Sec. IV.B. For d(mg)<dc the solutions for d and f saturate at low momentum (Figs. 4 and 5), so V(k) approaches a constant times 1/k^2, i.e. a Coulomb potential with no linear term; confinement appears only on the critical surface. The paper is explicit that 'we simply require that the theory give rise to an enhancement of the FP operator at small momentum, this boundary condition then selects the coupling d(mu)=dc', but the abstract's 'confinement ... emerge[s]' reads as unconditional. A concrete test would strengthen the case considerably: include the horizon term explicitly as Zwanziger does in Ref. [6] and verify that the self-consistent solution flows to dc rather than having dc imposed by hand. Relatedly, the justification in Sec. II.B for expanding the FP operator over all field space while claiming restriction to the fundamental modular region ('justified as long as the expectation value of the Faddeev-Popov operator does not change sign') is checked only a posteriori through d(0) tending to infinity; a short discussion of what would go wrong if configurations outside the FMR contributed with the opposite sign would help.
[Sec. III.F, Eqs. (96)-(104)] The truncation is not controlled in the regime where the confinement signal is generated. The power counting in d given after Eq. (53) assigns E(0),omega_C to O(d^2) and E(0),K_C to O(d^4), but at the selected critical point d(mg) is approximately 3.5 and d(k) grows toward the infrared as k^{-0.48} (Eq. 90), so the nominal expansion parameter is O(1) to O(3) precisely at low momentum. The O(d^4) check shown in Fig. 9 omits the Faddeev-Popov determinant contributions VA and VB of Eq. (104) and is explicitly described as preliminary, with the full study deferred to 'elsewhere'; the vertex estimate of Sec. III.F.1 uses the approximate analytical solutions and addresses only the triple vertex, not the higher irreducible vertices of the FP Dyson equation. Because the exponent 2ad+af=1.93 is what makes V(k) nearly k^{-4}, a modest shift in it would change the confining behavior. At minimum, an estimate of the omitted O(d^4) terms and a demonstration that dc and the exponent are stable against them should be provided, or the claim that the critical behavior is universal (Sec. III.D) should be softened to an expectation.
[Abstract and Sec. IV.A] The statement that 'the results agree remarkably well with lattice computations' overstates what is shown. The comparison in Fig. 10 is obtained by fitting f(mg)=1.41 and mg=1.4/r0=600 MeV to the lattice static potential, so it is a two-parameter fit to the same data, not a parameter-free prediction; the paper is transparent about this in Sec. IV.A, but the abstract is not. Furthermore, the same framework predicts a gap function omega(k) that is flat at low momentum, which the authors themselves note is inconsistent with the Cucchieri-Zwanziger lattice result for the transverse propagator (Sec. IV.B, Eq. 115). The abstract should state the fit explicitly and should present the lattice comparison as a partial success accompanied by a tension in omega(k), rather than as a blanket agreement. This matters because the lattice potential is the principal quantitative support for the central claim.

Minor objections (10)

[Sec. III.C, Eqs. (70)-(71) and (80)-(81)] The scheme yields beta-bar_0 = 8Nc/3, so that 3/2 beta-bar_0 = 4Nc = 12 for Nc=3, whereas the perturbative coefficient is 11Nc/3 = 11. The paper explains the difference as the omitted iteration of the Coulomb-transverse gluon vertex, and the numerical discrepancy is only about nine percent, so this is not a major concern; nevertheless a one-line estimate of how the missing screening piece would feed back into the infrared solution for d(k) would be useful, since the same diagrams are dropped everywhere in the resummation.
[Sec. III.D, Eq. (85)] The closed-form solution for k<mg involves an absolute value and a fractional power, d(k)^2/|3 - (5 beta-bar_0)/(3(4 pi)^2)(k/mg) d^2(k)|^{4/5}; please verify the exponent and the placement of the absolute value, and state explicitly the range of d(mg) over which the expression is real and positive.
[Sec. III.E, Eq. (93)] The string tension is extracted assuming exact linearity, 2ad+af=2, while the fit gives 1.93. The text calls the 3.5 percent difference negligible, which is plausible, but the quoted values mg approximately 530 MeV and 630 MeV inherit that assumption; a sentence quantifying the sensitivity of mg to the exponent would make the estimate more robust.
[Sec. IV.A, Eq. (107)] The analytical and numerical solutions give noticeably different parameter sets (f(mg) approximately 1.0 with mg approximately 1.8/r0 versus f(mg)=1.41 with mg=1.4/r0). It would help to state whether the two fits are equally acceptable to the lattice data or whether one is preferred, since this bears on how much of the agreement is driven by the fit.
[Sec. V.A] The assertion that 'all color singlets are IR finite' while colored states are removed is central to the argument that H0 generates a usable hadronic basis, but it is stated without proof or reference. A short argument, or a pointer to where it is demonstrated, would strengthen this section.
[Sec. V.B] Casimir scaling is presented as a clean prediction of the leading kernel, but lattice measurements show it is only approximate and is violated at large separation by string breaking. The text should acknowledge the expected range of validity rather than presenting the scaling as exact.
[Sec. V.D and Ref. [12]] The argument that the vector-pseudoscalar splitting follows a CQM-like form rests on Ref. [12], which is cited as 'to appear Phys. Rev. Lett.'; the citation should be updated to the published version, and Ref. [24] (hep-th/0012024), used for the transverse-propagator comparison in Sec. IV.B, should likewise be checked for a published version.
[Equations and typography] Several equations need cleaning: Eq. (33) has a stray comma in 'K ab(x, y; A)Lambda, ='; Eqs. (38) and (47) write 'd2(K, Lambda)' where 'd2(k, Lambda)' is presumably meant; Eq. (94) has an unbalanced parenthesis in 'd(k + l - q)k + l - q)^2'; Eqs. (102) and (103) carry two equation numbers for a single displayed equation, the second of which is empty; and Eq. (95) would be easier to parse if the color-index structure were spelled out explicitly for n=2. The manuscript also contains numerous broken words and spacing artifacts (for example 'particula r', 'conﬁgur ations', 's ince') that should be removed before publication.
[Sec. III.D] The sentence 'One expects; however, that the critical behavior is universal' uses a semicolon where a comma is intended, and the surrounding passage would read more clearly if the expectation were separated from the demonstrated result.
[Fig. 6] The vertical axis label 'omega(k)/omega(0) = omega(k)/mg' is redundant; a single form would suffice, with the identification omega(0)=mg stated once in the text.

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The paper

The paper claims

A single self-consistent Coulomb-gauge calculation produces both confinement and the constituent quark picture, with a nearly linear static potential emerging from an infrared-enhanced Faddeev-Popov operator.

The reading

The paper asks whether two of the oldest puzzles in strong-interaction physics — why quarks are confined, and why they behave as heavy, weakly interacting constituent particles inside hadrons — can be answered by one controlled calculation rather than by two separate models. Working in Coulomb gauge, where the instantaneous force between colour charges is explicit and all degrees of freedom are physical, the authors build a variational Gaussian vacuum and derive three coupled equations: one for the vacuum expectation of the Faddeev-Popov operator $d(k)$, one for the Coulomb kernel $f(k)$, and one for the gluon gap function $omega(k)$. Solving them self-consistently, they find that at a critical coupling the Faddeev-Popov operator is enhanced at small momentum, which drives the effective colour-Coulomb interaction $V(k)=f(k)d^2(k)/k^2$ to scale as $k^{-1.93}$ — close enough to $1/k^2$ to give a nearly linear confining potential, while the gluon gap function stays finite at $k=0$, giving transverse gluons an effective mass of roughly 600–700 MeV. The Fourier-transformed potential tracks the lattice static quark–antiquark potential with only two free parameters, and the same variational vacuum that produces confinement also produces massive quasiparticles, so the constituent degrees of freedom of the quark model appear as the natural excitations of the confining vacuum rather than as an unrelated phenomenological input.

What carries the argument

The load-bearing object is the coupled system of three gap equations: Eq. (63) for the vacuum expectation of the Faddeev-Popov operator $d(k)$, Eq. (65) for the Coulomb kernel $f(k)$, and Eq. (67) for the gluon gap function $omega(k)$, obtained by minimising the vacuum energy density of a Gaussian ansatz $Psi_0[A] = exp[-tfrac{1}{2}int A omega A]$ with respect to $omega$. The link between them is the Swift equation, which expresses the instantaneous nonabelian Coulomb kernel as a logarithmic derivative of the Faddeev-Popov operator with respect to the coupling, $K^{ab}(x,y;A) = g^2 (d/dg) langle x,a| g nabla cdot D |y,b rangle$. Expanding the Faddeev-Popov operator in powers of $gA$ around the variational vacuum and resumming the rainbow-ladder series turns the Coulomb kernel into a functional of $d(k)$ and $omega(k)$, which is what makes the problem self-consistent rather than a one-pass calculation. The renormalisation analysis is the second piece of machinery: the authors show that the triple Coulomb-transverse-gluon vertex needs no renormalisation ($Z_1 = 1$), that the gap equation needs only a single subtraction, and that all counterterms run as functions of one coupling $g(Lambda)$ with a one-loop coefficient $bar{beta}_0 = 8N_c/3$.

Extended reading notes

Core claim

The central claim is that confinement and the constituent representation are two faces of one object: the expectation value of the Faddeev-Popov operator in a self-consistent variational vacuum. Because the nonabelian Coulomb kernel depends on the gauge field, the interaction used to define the vacuum and the vacuum used to define the interaction must be solved together. The authors truncate the resulting tower of equations at rainbow-ladder level and solve numerically, finding an infrared critical point at $d(m_g) = d_c approx 3.5$ where $d(k) propto (m_g/k)^{0.48}$ and $f(k) propto (m_g/k)^{0.97}$, so that the colour-Coulomb potential $V(k) = f(k)d^2(k)/k^2$ falls off as $k^{-1.93}$. A $1/k^2$ falloff Fourier-transforms to a linear confining potential; the fitted exponent misses by roughly 3.5%, which the authors attribute to discretisation or truncation and call negligible for phenomenology. Imposing exact linearity, $2a_d + a_f = 2$, fixes the scale through $6pi b = (3.5)^2 m_g^2$, giving $m_g approx 530$ MeV for the quark-model string tension $b = 0.18$ GeV$^2$ and $m_g approx 630$ MeV for the lattice value $b = 0.26$ GeV$^2$; a direct fit to lattice Wilson-loop data gives $f(m_g) = 1.41$ and $m_g = 1.4/r_0 approx 600$ MeV. The authors read the critical point as the dynamical realisation of the Gribov-Zwanziger scenario: the infrared singularity of the Faddeev-Popov operator required by the horizon condition is exactly the boundary condition that selects $d(mu) = d_c$. They further argue that because the same vacuum generates a mass gap, the Fock-space expansion of hadrons converges quickly in quasiparticle states, which explains the long-observed success of the constituent quark model and resolves several of its internal inconsistencies.

Load-bearing premise

The confinement result depends on sitting exactly at a critical coupling $d(m_g) = d_c approx 3.5$, and that value is not derived — it is selected by requiring that the Faddeev-Popov operator develop the Gribov-Zwanziger infrared singularity, so if the true solution sits below the critical point the operator saturates at a finite value and the near-linear potential disappears.

Editorial extensions

If this is right

Confinement in the heavy-quark limit follows from the instantaneous Coulomb operator alone, with no need for a separate confining mechanism, because the transverse gluon sector decouples as quarks get heavy.
The confining kernel has colour structure $K^{(0)ab} = delta^{ab}K^{(0)}$, so the static potential between colour sources scales as the quadratic Casimir — the observed Casimir scaling of Wilson-loop potentials becomes a prediction rather than an input.
Confinement acts as the time component of a vector interaction, not a scalar one, which removes the long-standing inconsistency in which scalar confinement binds mesons but antibinds baryons.
The authors argue that the '$^3P_0$' pair-creation vertex used phenomenologically for strong decays arises microscopically from the product of the first-order Coulomb kernel $K^{(1)}$ with the quark-gluon coupling, giving a $psi^dagger[sigma delta_T nabla]psi$ operator.
Quark masses saturate near 200 MeV as the bare mass goes to zero, and light-quark loops only renormalise the string tension, so the same framework is claimed to survive, at least qualitatively, for light flavours.

Reading between the lines

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

If the critical coupling is a genuine fixed point rather than an artefact of the rainbow-ladder truncation, then the confinement scale and the gluon mass gap are not independent parameters but two readings of one number, which would remove a free parameter from low-energy QCD phenomenology.
The paper's own comparison shows the transverse gluon propagator $1/(2omega(k))$ is flatter at low momentum than the lattice measurement it is compared to; a lattice determination of $omega(k)$ with controlled systematic errors would therefore discriminate between this vacuum ansatz and the true Coulomb-gauge ground state more sharply than the static potential does, since the potential is fitted.
Because the mechanism ties confinement to the positivity of the Faddeev-Popov operator, the same machinery should predict how the string tension and gluon mass move with temperature or with quark density — a direction the paper flags in a footnote but does not pursue.
The claim that the '$^3P_0$' decay vertex is generated rather than assumed is testable: it implies specific relative phases and momentum dependence in the pair-creation amplitude that differ from the phenomenological model's constant strength.

Original abstract

Quark confinement and the genesis of the constituent quark model are examined in nonperturbative QCD in Coulomb gauge. We employ a self-consistent method to construct a quasiparticle basis and to determine the quasiparticle interaction. The results agree remarkably well with lattice computations. They also illustrate the mechanism by which confinement and constituent quarks emerge, provide support for the Gribov-Zwanziger confinement scenario, clarify several perplexing issues in the constituent quark model, and permit the construction of an improved model of low energy QCD.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,578 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

Quark confinement and the genesis of the constituent quark model are examined in nonperturbative QCD in Coulomb gauge. We employ a self-consistent method to construct a quasiparticle basis and to determine the quasiparticle interaction. The results agree remarkably well with lattice computations. They also illustrate the mechanism by which confinement and constituent quarks emerge, provide support for the Gribov-Zwanziger confinement scenario, clarify several perplexing issues in the constituent quark model, and permit the construction of an improved model of low energy QCD.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Quark confinement and the genesis of the constituent quark model are examined in nonperturbative QCD in Coulomb gauge.	contribution 0.65	0.59	0.07	asserted 0.70
s1	We employ a self-consistent method to construct a quasiparticle basis and to determine the quasiparticle interaction.	method 0.99	0.94	0.04	asserted 0.97
s2	The results agree remarkably well with lattice computations.	result 1.00	0.85	0.11	asserted 1.00
s3	They also illustrate the mechanism by which confinement and constituent quarks emerge, provide support for the Gribov-Zwanziger confinement scenario, clarify several perplexing issues in the constituent quark model, and permit the construction of an improved model of low energy QCD.	interpretation 0.98	0.88	0.84	asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.62 · evidence from simulation or computation 0.93.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1. Dyson equation of the Coulomb-transverse gluon vert

**Figure 2.** FIG. 2. Dyson equation for Γ

**Figure 3.** −1 = g 1 − g FIG. 3. Dyson equation for the VEV of the Faddeev-Popov operator. See

**Figure 4.** FIG. 4. Solution for the expectation value of the FP operator

**Figure 6.** FIG. 6. Comparison of the analytical approximation to

**Figure 7.** FIG. 7. Numerical solution for

**Figure 9.** FIG. 9. Normalized instantaneous transverse gluon propaga

**Figure 11.** FIG. 11. The leading light quark correction to the confinemen

**Figure 12.** FIG. 12. Examples of Higher Order Corrections to the Heavy Qu

**Figure 13.** FIG. 13. Leading Order in 1

**Figure 14.** FIG. 14. Light Quark Loop Correction to the Heavy Quark-Anti

Showing 12 of the paper's 14 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0107078 by the authors.

References

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Effects of divergent ghost loops on the Green's functions of QCD
hep-ph 2013-12 conditional novelty 5.0 of 10

The nonperturbative masslessness of the ghost field produces infrared divergences in the gluon kinetic term that explain the peak in the gluon propagator and the negative divergence of the three-gluon vertex projector.
Non-perturbative Landau gauge and infrared critical exponents in QCD
hep-th 2001-09 conditional novelty 5.0 of 10

A stochastic-quantization derivation of non-perturbative Landau gauge yields Faddeev-Popov theory plus a Gribov-copy over-counting correction, and truncated Schwinger-Dyson equations give infrared gluon and ghost expo...
Nonperturbative properties of Yang-Mills theories
hep-ph 2018-08 accept novelty 3.0 of 10

Functional equations now give self-consistent gluon and ghost propagators and vertices in Landau gauge Yang-Mills theory, including two-loop diagrams, with truncation dependence that is quantitative rather than qualit...
The Gribov problem and QCD dynamics
hep-th 2012-02 conditional novelty 3.0 of 10

The review consolidates the Gribov-Zwanziger approach to confinement, showing how a horizon-restricted, local, renormalizable action yields a gluon propagator with unphysical poles, while documenting where its predict...
Infrared Properties of QCD from Dyson-Schwinger equations
hep-ph 2006-05 accept novelty 3.0 of 10

Landau-gauge Dyson-Schwinger studies indicate an infrared-finite running coupling, a vanishing gluon propagator, and dynamically generated quark mass, though lattice and continuum results still differ at low momentum.
The QCD Running Coupling
hep-ph 2016-04 accept novelty 2.0 of 10

A comprehensive review of the QCD running coupling across perturbative and nonperturbative regimes, closing with a proposal that effective charges defined directly from observables give the most unified definition of alpha_s.

How the literature uses it

86 arXiv papers cite this in 135 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 68 sentences without a confident label

Uses its method or tool 2 papers

The ensuing Schwinger-Dyson equations can be truncated and solved to obtain estimates for the vacuum expectation of the kernel, $K̂^AB$, and for the gluon dispersion relationship [ref] .

Light Hybrid Meson Mixing and Phenomenology · Model Construction · 0.84
Noticing that the interest of this work is focused on the spectrum of $qq̅$ states, our starting point is an effective version of the Coulomb gauge QCD Hamiltonian [ref] .

Revisiting the tensor $J^{PC} = 2^{--}$ meson spectrum · The formalism · 0.95

Uses its data or values 1 paper

The solution is typically well approximated by $ω(q)=m_g$ for $q≤m_g$ and by $ω(q)=q$ for $q>m_g$, with the constituent gluon mass given by $m_g≃600$ [ref] .

Multiquark Resonances · Modeling the hybrids: constituent gluons in Coulomb gauge · 0.98

Compares with it 4 papers

In the following we analyze the full set of equations, explain why in [ref] it was possible to find an IR vanishing gluon propagator while it was not the case for the solution found in [ref] , and present a full set of numerical solutions to all three equations.

Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge · Variational Coulomb QCD · 0.86
In this appendix we compare our results for the ghost and Coulomb propagators derived from lattice simulations with the predictions of Dyson-Schwinger (DS) equations [ref] .

Constituent gluons and the static quark potential · Comparison with Dyson-Schwinger equations · 1.00
Indeed, comparing this Hamiltonian with that of Christ and Lee [ref] , or in recent papers [ref] , one notices the absence of the Faddeev-Popov determinant in our expression.

Boost operators in Coulomb-gauge QCD: the pion form factor and Fock expansions in phi radiative decays · The Hamiltonian and Momentum Generators of a pure Yang-Mills theory · 0.99

Cites it as support 2 papers

For example, in Refs. [ref] , linear confinement was obtained as a result of variational calculations in quenched Coulomb-gauge QCD; see also Ref. [ref] for recent insights and relevant references.

Confined but chirally and chiral spin symmetric hot matter · Hamiltonian of the model · 0.97
This implies an additive momentum-dependent mass renormalization in the quark propagator [ref] , which is also reported within the Hamiltonian formalism of QCD in Coloumb gauge [ref] .

Asymptotically conformal CFL quark matter within a nonlocal chiral quark model · Introduction · 0.97

Cites it as background 48 papers

Recently progress has been made in variationally solving the Yang-Mills Schrödinger equation in Coulomb gauge [ref] .

The 't Hooft loop in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge · Introduction · 0.82
Among these are functional renormalization group (FRG) equations [ref] and the variational approach to the Hamiltonian formulation of QCD [ref] .

Hamiltonian Flow of Yang-Mills Theory in Coulomb Gauge · Introduction · 0.98
In recent years the vacuum sector of Yang–Mills theory was treated within the Hamiltonian approach in Coulomb gauge using the variational principle [ref] .

Revised variational approach to QCD in Coulomb gauge · Introduction · 0.99

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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