Ultraviolet modifications of dispersion relations in effective field theory

Maxim Pospelov; Robert C. Myers

REVIEW

Ultraviolet modifications of dispersion relations in effective field theory

Robert C. Myers, Maxim Pospelov

High Energy Physics - Phenomenology · Submitted 17 Jan 2003 · 13 references

Pith's verdict: The dimension-five operator classification is correct and genuinely corrects the chirality-blind E^3/M_Pl ansatz, but the abstract's uniform 10^-5/M_Pl bound papers over an order-one direct electron limit that only an unshown RG running improves.

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arXiv IDhep-ph/0301124 (version 2)

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CitationMaxim Pospelov, Robert C. Myers. "Ultraviolet modifications of dispersion relations in effective field theory." arXiv:hep-ph/0301124 (2003). https://pith.science/paper/RSRXMYHJ

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Editor's note

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The operator classification is the real contribution here, and it holds up. Section II does what it claims: with Lorentz breaking carried by a fixed timelike n^a, there is one dimension-five operator for a complex scalar, one for U(1), and two for a Dirac fermion, after the equations-of-motion and total-derivative exclusions are applied. I checked the counting and the algebra; the chirality dependence falls out correctly, sign flip with photon circular polarization, eta_L versus eta_R splitting for fermions. The consequence is worth the paper: the chirality-blind E^3/M_Pl dispersion relation that the gamma-ray-burst and synchrotron literature assumes is not what effective field theory gives you. That is a genuine correction to the prior phenomenology, and the authors are right to press it. For anyone working on Planck-scale Lorentz violation this is the part that will last, and it will be cited. The bounds section is looser than the abstract admits. abstract:s2 advertises a uniform 10^-5/M_Pl for electrons, photons and light quarks. Sector by sector: quarks come out at 10^-8 (Eq. 14), photons at 10^-5, but the direct electron bound, Eq. (11), is order one, |eta_eL - eta_eR| <~ 4. The 10^-5 electron figure appears only through a one-loop running the paper defers with 'Leaving the details for elsewhere' and no reference. The introduction does flag this as an RG improvement, so it is not concealed, but the abstract flattens three different numbers into one, and the electron is exactly where the direct data are weakest. Tighten the abstract. The rest of Section III is order-of-magnitude and reasonably candid about it: a_u,d and b_u,d quoted from structure functions, b_gamma from naive vector dominance, |n^i| ~ 10^-3 assumed, no uncertainties propagated. Fine for a Letter, but read the numbers as central values. On the C^abc substitution, the reader's worry is technically right, C^000 = n_0^3 - n_0/2 is an O(1) shift in the nonrelativistic coefficient, but it does not move an order-one bound, and the E >> m dispersion relations are indeed untouched because the trace part is m^2-suppressed. Minor. Worth a serious referee report; the classification is solid and the bounds need the abstract brought into line with Eq. (11).

Referee report

Major objections (4)

[Abstract (abstract:s2); Section III, Eq. (11) and closing paragraph] The abstract states that clock comparison experiments bound these operators at 10^-5/M_Pl for electrons, photons and light quarks, but the direct analysis gives sector-dependent numbers: Eq. (11) gives |eta_eL - eta_eR| <~ 4, i.e. order one, for electrons; Eq. (14) gives about 10^-8 for quarks; and xi is bounded at about 10^-5 for photons. The 10^-5 electron figure appears only in the closing paragraph as an RG-improved result introduced with 'Leaving the details for elsewhere' and with no reference. The introduction itself states the sector-by-sector result correctly ('O(1) limits for leptons, O(10^-5) for photons and O(10^-8) for quarks'), so the abstract is inconsistent with the body of the paper. Either supply the RG details or a reference for them, or restate the abstract to match Section III.
[Section II, technical aside on the C^abc substitution] The justification that the substitution n^a n^b n^c -> C^abc 'does not affect the dispersion relations in the regime E >> m' is correct for the E >> m dispersion relations, but the bounds in Section III are derived in the nonrelativistic regime, where the m_e^2 in Eq. (11) comes from (n^0 d_t)^2 acting on the electron wavefunction. Under the substitution C^{000} = n_0^3 - n_0/2, an O(1) change in the coefficient that sets the bound. The paper should show explicitly that the nonrelativistic coefficients entering Eqs. (11) and (14) are unchanged, or state the O(1) ambiguity. Numerically this does not alter the order-one electron bound, but it should be stated rather than left implicit.
[Section III, Eqs. (13)-(14)] The nucleon matrix elements a_u,d and b_u,d are quoted as numbers (a_d ~ 0.4, a_u ~ 0.1, b_d ~ 0.1, b_u ~ -0.05) with only the remark that they 'could be obtained as the moments of the experimentally measured structure functions', and b_gamma ~ 0.13 alpha/(4 pi) comes from a vector-dominance estimate. The 10^-8 quark bound depends on these quantities. Please cite the source of the moments and quantify the model uncertainty in b_gamma. In addition, Eq. (14) bounds only one combination; the statement that 'barring accidental cancellations, one can place separate limits on eta_u,d - eta_Q at 10^-8' is a caveat rather than a derivation and should be presented as such.
[Abstract (abstract:s1) versus Section II] The abstract says the operators 'do not mix with dimensions 3 and 4', but Section II shows that the eta2 operator generates a dimension-three operator Lambda_UV^2 M_Pl^{-1} psi-bar n-slash gamma5 psi at one loop. Non-mixing holds only after the C^abc projection, which is a scheme choice removing the divergent vector part. The abstract should carry this qualification so that it is not read as a statement about the unprojected operators.

Minor objections (5)

[Section II] There are two occurrences of 'effect' where 'affect' is intended: 'does not effect the dispersion relation in a significant way' and 'these would not effect the threshold tests'.
[Section II, Eqs. (10)-(11)] The relation between eta1, eta2 and the chiral couplings eta_eL, eta_eR should be stated explicitly (eta_eL - eta_eR = 2 eta2), since Eq. (11) is written in the chiral basis while Eq. (7) is written in the Dirac basis.
[Section III, Eq. (12)] The operator as written is chirality-diagonal; for the left-handed doublet psi_Q the appropriate projection should be displayed, since the matching in Eq. (13) assumes definite chiral couplings.
[Section II, discussion of prior work] The statement that 'the commonly studied dispersion relations [2-4] do not conform with those derived here' would be more useful with one sentence spelling out what the effective field theory predicts for the leading correction in each case, so the reader can see the discrepancy without reconstructing it.
[Section II, scalar case] The statement that the cubic modification is impossible for the Higgs is correct but rests on the real-scalar total-derivative argument; a one-line reminder at the point of use would help the reader.

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The paper

The paper claims

The paper argues that if a Planck-scale preferred frame modifies particle dispersion relations, ordinary effective field theory allows only a handful of dimension-five operators — one for a complex scalar, one for the photon, two for a ferm

The reading

The paper asks a narrow, answerable version of a broad question: if quantum gravity introduces a preferred frame at the Planck scale, what corrections to particle dispersion relations can ordinary effective field theory actually produce? Requiring each new term to be quadratic in the field, gauge invariant, one derivative beyond the standard kinetic term, and not removable by the equations of motion or a total derivative leaves very few options: one operator for a complex scalar, one for the photon, and two for a Dirac fermion, all giving corrections of order $E^3/M_{Pl}$. The authors emphasise that these operators do not look like the chirality-blind $E^3/M_{Pl}$ corrections often postulated in the quantum-gravity phenomenology literature: the photon correction flips sign with circular polarization, and left- and right-handed fermions carry independent couplings. Because the preferred frame cannot coincide with the laboratory frame, the Earth's motion ($|n_i|$ of order $10^{-3}$) turns these operators into small spatial anisotropies, which existing clock-comparison and spin-precession experiments already constrain. The authors state plainly that assuming dimension-three and four operators are absent has serious theoretical problems, and that a symmetry would be needed to forbid them; they proceed because those operators are already tightly bounded by experiment.

What carries the argument

The load-bearing device is the operator classification itself: a fixed timelike background four-vector $n^a$ (with $n·n = 1$) supplies the open Lorentz indices, and six filters — quadratic in the same field, exactly one extra derivative, gauge invariant, Lorentz invariant except for $n^a$, irreducible by the leading equations of motion, and not a total derivative — cut the list down to four operators across scalars, vectors and fermions. The second piece of machinery is a technical fix: the tensor $n^a n^b n^c$ is replaced by its traceless symmetric part $C^{abc} = n^a n^b n^c - (1/6)(n^a g^{bc} + cyclic)$, because the trace part generates quadratic divergences that would regenerate dimension-three operators such as $Λ_{UV}^2 M_{Pl}^{-1} ψ̄ n̸γ_5ψ$ and drag the coefficients below $10^{-10}$ through existing bounds. The authors assert that this substitution leaves the dispersion relations unchanged for $E gg m$.

Extended reading notes

Core claim

The central claim is a classification plus a set of bounds. With Lorentz symmetry broken only by a fixed timelike four-vector $n^a$, the authors identify the complete set of dimension-five operators that survive their six criteria and that shift the dispersion relation at cubic order. For a complex scalar there is one, $i(κ/M_{Pl})Φ̄(n·∂)^3Φ$, which is odd under CPT and charge conjugation; for a real scalar such as the Standard Model Higgs it is a total derivative and does nothing. For a $U(1)$ gauge field there is exactly one, $L_γ = (ξ/M_{Pl}) n_a F^{ad} n·∂(n_b F̃^b{}_d)$, which is CPT-odd and charge-conjugation even and gives $E^2 - p^2 ± 2ξ p^3/M_{Pl} = 0$ for the two circular polarizations, so linearly polarized light rotates its plane of polarization. For a Dirac fermion there are two, $L_f = (1/M_{Pl})Ψ̄(η_1 n̸ + η_2 n̸γ_5)(n·∂)^2Ψ$, giving an $E^3$ shift proportional to $η_1 + η_2γ_5$, i.e. separate couplings $η_{R,L} = η_1 ± η_2$ for the two chiralities. The authors conclude that the commonly studied chirality-independent cubic dispersion relation is not what effective field theory yields. They then translate terrestrial limits: electron spin-precession data give $|η^e_L - η^e_R| ≲ 4$ (weak, because the effect is suppressed by $m_e^2$), nuclear-spin clock comparison gives $|(η_d - η_Q) - 0.5(η_u - η_Q) + 10^{-3}ξ| ≲ 10^{-8}$, and separately $|ξ| ≲ 10^{-5}$, all in units of $1/M_{Pl}$; a one-loop renormalization-group analysis tightens the quark and photon coefficients to about $10^{-6}$ and the lepton coefficients to about $10^{-5}$.

Load-bearing premise

The bounds rest on replacing $n^a n^b n^c$ with the traceless symmetric tensor $C^{abc}$ to suppress quadratic divergences, together with the paper's assertion that this replacement 'does not affect the dispersion relations in the regime $E gg m$' — even though the electron bound in Eq. (11) is derived in the nonrelativistic regime, where the $m_e^2$ factor from $(n^0∂_t)^2$ sets the size of the effect and the paper does not show the substitution leaves that coefficient unchanged.

Editorial extensions

If this is right

Any cubic correction from a Planck-scale preferred frame must flip sign between the two photon circular polarizations, so polarimetry of distant sources — not a simple time-of-flight lag — is the natural observational probe of the photon operator.
The Higgs boson cannot receive a cubic dispersion correction at all, because for a real scalar the only candidate operator is a total derivative.
Fermion corrections come in two independent chirality couplings, so fits to astrophysical data that assume a single common coefficient constrain only one combination of $η_1$ and $η_2$.
Existing clock-comparison and spin-precession data already bound the photon coefficient at about $10^{-5}/M_{Pl}$ and the light-quark combinations at about $10^{-8}/M_{Pl}$, roughly an order of magnitude better than the birefringence bound the paper cites.
Running the coefficients from the Planck scale down to 1 GeV with one-loop renormalization-group equations strengthens the quark and photon limits to about $10^{-6}$ and the lepton limits to about $10^{-5}$.

Reading between the lines

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

Because the anisotropy is fed by the Earth's velocity relative to the preferred frame, these operators should appear as sidereal-time modulation in atomic clock comparisons; re-analysing existing clock data for that modulation would test the classification without new apparatus.
The classification is a statement about operators, not about any particular quantum-gravity model, so any candidate theory predicting a cubic dispersion relation can be mapped onto one of these few coefficients and confronted with the quoted bounds immediately.
If the traceless-tensor substitution is not innocuous at low energies, the electron bound in Eq. (11) could move by mass-suppressed factors, which would change how sharply the loop-quantum-gravity fermion predictions are excluded.
The same operator list applies to any light beyond-Standard-Model fermion or vector, so the bounds can be re-read as constraints on new light particles that couple to the preferred frame.

Original abstract

The existence of a fundamental ultraviolet scale, such as the Planck scale, may lead to modifications of the dispersion relations for particles at high energies, in some scenarios of quantum gravity. We apply effective field theory to this problem and identify dimension 5 operators that do not mix with dimensions 3 and 4 and lead to cubic modifications of dispersion relations for scalars, fermions, and vector particles. Further we show that, for electrons, photons and light quarks, clock comparison experiments bound these operators at 10^{-5}/Mpl.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.22 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.16 · mentions code or data availability 0.01.

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The existence of a fundamental ultraviolet scale, such as the Planck scale, may lead to modifications of the dispersion relations for particles at high energies, in some scenarios of quantum gravity. We apply effective field theory to this problem and identify dimension 5 operators that do not mix with dimensions 3 and 4 and lead to cubic modifications of dispersion relations for scalars, fermions, and vector particles. Further we show that, for electrons, photons and light quarks, clock comparison experiments bound these operators at 10^{-5}/Mpl.

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	The existence of a fundamental ultraviolet scale, such as the Planck scale, may lead to modifications of the dispersion relations for particles at high energies, in some scenarios of quantum gravity.	background 1.00	0.05	0.08	hedged possibility 1.00
s1	We apply effective field theory to this problem and identify dimension 5 operators that do not mix with dimensions 3 and 4 and lead to cubic modifications of dispersion relations for scalars, fermions, and vector particles.	contribution 0.86	0.95	0.24	asserted 1.00
s2	Further we show that, for electrons, photons and light quarks, clock comparison experiments bound these operators at 10^{-5}/Mpl.	result 0.99	0.84	0.57	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.82.

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sources read

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References

Works cited (13)

[1]

D. Colladay and V.A. Kostelecky, Phys. Rev. D55 (1997) 6760; S.R. Coleman and S.L. Glashow, Phys. Rev. D59 (1999) 116008; S.M. Carroll, G.B. Field and R. Jackiw, Phys. Rev. D41 (1990) 1231

View on Pith 1997
[2]

G. Amelino-Camelia et al. , Nature 393 (1998) 763; G. Amelino-Camelia and T. Piran, Phys. Rev. D64 (2001) 036005; G. Amelino-Camelia, Phys. Lett. B528 (2002) 181; S. Sarkar, Mod. Phys. Lett. A17 (2002) 1025

View on Pith 1998
[3]

T. Jacobson, S. Liberati and D. Mattingly, Phys. Rev. D66 (2002) 081302; hep-ph/0209264; T.J. Konopka and S.A. Major, New J. Phys. 4 (2002) 57

View on Pith Pith review arXiv 2002
[4]

T. Jacobson, S. Liberati and D. Mattingly, astro- ph/0212190

View on Pith
[5]

R.J. Gleiser and C.N. Kozameh, Phys. Rev. D64 (2001) 083007

View on Pith 2001
[6]

G. Amelino-Camelia, Nature 398 (1999) 216; I. Mo- cioiu, M. Pospelov and R. Roiban, Phys. Lett. B489 (2000) 390; G.Z. Adunas, E. Rodriguez-Milla and D.V. Ahluwalia, Phys. Lett. B485 (2000) 215; R. Bluhm, hep-ph/0111323

View on Pith Pith review arXiv 1999
[7]

D. Sudarsky, L. Urrutia and H. Vucetich, Phys. Rev. Lett. 89 (2002) 231301

View on Pith 2002
[8]

I.Mocioiu and M.Pospelov, Phys. Lett. B534 (2002) 114

View on Pith 2002
[9]

T.E. Chupp et al., Phys. Rev. Lett. 72, 2363 (1994); R.E. Stoner et al. , Phys. Rev. Lett. 77, 3971 (1996); D. Bear et al. , Phys. Rev. A57, 5006 (1995); C.J. Berglund et al. , Phys. Rev. Lett. 75, 1879 (1995); D. Bear, et al. Phys. Rev. Lett. 85 (2000) 5038 [Errat. 89 (2002) 209902]

View on Pith 1994
[10]

E.G. Adelberger et al. , in Physics Beyond the Stan- dard Model, 1998, Santa Fe (World Scientiﬁc, Singapore, 1999); M.G. Harris, PhD Thesis, University of Washing- ton, 1998; B.R. Heckel et al. , in Proceedings of the In- ternational Conference on Orbis Scientiae, 1999, Coral Gables (Kluwer, New York, 2000)

View on Pith 1998
[11]

R. Gambini and J. Pullin, Phys. Rev. D59 (1999) 124021; J. Alfaro, H.A. Morales-Tecotl and L.F. Urrutia, Phys. Rev. D65 (2002) 103509

View on Pith 1999
[12]

J. Alfaro, H.A. Morales-Tecotl and L.F. Urrutia, hep- th/0208192

View on Pith
[13]

H. Sahlmann and T. Thiemann, gr-qc/0207030; gr- qc/0207031. 4

View on Pith Pith review arXiv

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How the literature uses it

72 arXiv papers cite this in 121 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 · 79 sentences without a confident label

Builds on it 2 papers

This is the Myers-Pospelov operator [ref] suitably extended in the present study to affect the superluminality behavior at large momenta.

Superluminal neutrinos from Lorentz-violating dimension-5 operators · Introduction · 0.97
This problem is just a generalization of the issue of (Lorentz-violating) Modified Dispersion Relations (MDR) considered in the past for the standard model alone, with gravity being switched off [ref] (see also [ref] for an earlier proposal).

A note on particle kinematics in Horava-Lifshitz scenarios · Introduction · 0.86

Uses its method or tool 1 paper

For the case of QED, an approach similar to that of Myers & Pospelov [ref] was taken.

New constraints on Planck-scale Lorentz Violation in QED from the Crab Nebula · QED with Lorentz Violations at order $O(E/M)$ · 0.92

Uses its data or values 1 paper

By analyzing the electromagnetic radiation from the Crab Nebula, the relevant parameters for order 5 terms in an extension of quantum electrodynamics [ref] have been constrained to $ξ< O(10^-7)$ and $| η_± | < O(10^-5)$ [ref] .

Experimental Search for Quantum Gravity · Astrophysics · 0.85

Compares with it 3 papers

Up to one order of magnitude these bounds approach those derived from renormalization group equations [ref] — see also [ref] for other bounds via dimension-4 operators in purely space-like backgrounds.

Superluminal neutrinos from Lorentz-violating dimension-5 operators · Introduction · 1.00
The $ξ_1$ type of coupling is similar in structure to the form $1/E_P n^α F_ασ n ·∂(n_β F̃^βσ)$ proposed by Myers and Pospelov [ref] motivated by quantum gravity arguments.

Constraints on background torsion from birefringence of CMB polarization · Introduction · 0.84
This is an important feature of our stringy approach, differentiating it from models that attribute time delays to modified dispersion relations obtained from a local effective lagrangian, such as the modified QED Model of [ref] .

Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model · A D-Brane Model for the Vacuum Refractive Index · 0.97

Cites it as background 34 papers

Many theories of quantum gravity predict non-trivial vacuum refractive indices, varying linearly with the energy scale of photons and with the distance of the source: see [ref] .

Probing a Possible Vacuum Refractive Index with Gamma-Ray Telescopes · Introduction · 0.80
A rich phenomenological program was developed over the last decade on the basis of results for models of spacetime quantization suggesting that (see, e.g., [ref] ) it is possible for the quantum properties of spacetime to introduce small violations of the special relativistic properties of classical spacetime.

Quantum-spacetime scenarios and soft spectral lags of the remarkable GRB130427A · A scenario for quantum spacetime · 0.93
The most studied [ref] modelization of quantum-gravity-induced in-vacuo dispersion is [equation] which in terms of $E^*$ takes the form [equation] $M_P$ denotes the Planck scale ($≃1.2 10^28eV$) and the values of the parameters $η_X$ and $δ_X$ in ([ref]) are to be determined experimentally.

In-vacuo-dispersion-like spectral lags in gamma-ray bursts · Introduction · 0.94

Discussion

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[1] [1]

D. Colladay and V.A. Kostelecky, Phys. Rev. D55 (1997) 6760; S.R. Coleman and S.L. Glashow, Phys. Rev. D59 (1999) 116008; S.M. Carroll, G.B. Field and R. Jackiw, Phys. Rev. D41 (1990) 1231

View on Pith 1997

[2] [2]

G. Amelino-Camelia et al. , Nature 393 (1998) 763; G. Amelino-Camelia and T. Piran, Phys. Rev. D64 (2001) 036005; G. Amelino-Camelia, Phys. Lett. B528 (2002) 181; S. Sarkar, Mod. Phys. Lett. A17 (2002) 1025

View on Pith 1998

[3] [3]

T. Jacobson, S. Liberati and D. Mattingly, Phys. Rev. D66 (2002) 081302; hep-ph/0209264; T.J. Konopka and S.A. Major, New J. Phys. 4 (2002) 57

View on Pith Pith review arXiv 2002

[4] [4]

T. Jacobson, S. Liberati and D. Mattingly, astro- ph/0212190

View on Pith

[5] [5]

R.J. Gleiser and C.N. Kozameh, Phys. Rev. D64 (2001) 083007

View on Pith 2001

[6] [6]

G. Amelino-Camelia, Nature 398 (1999) 216; I. Mo- cioiu, M. Pospelov and R. Roiban, Phys. Lett. B489 (2000) 390; G.Z. Adunas, E. Rodriguez-Milla and D.V. Ahluwalia, Phys. Lett. B485 (2000) 215; R. Bluhm, hep-ph/0111323

View on Pith Pith review arXiv 1999

[7] [7]

D. Sudarsky, L. Urrutia and H. Vucetich, Phys. Rev. Lett. 89 (2002) 231301

View on Pith 2002

[8] [8]

I.Mocioiu and M.Pospelov, Phys. Lett. B534 (2002) 114

View on Pith 2002

[9] [9]

T.E. Chupp et al., Phys. Rev. Lett. 72, 2363 (1994); R.E. Stoner et al. , Phys. Rev. Lett. 77, 3971 (1996); D. Bear et al. , Phys. Rev. A57, 5006 (1995); C.J. Berglund et al. , Phys. Rev. Lett. 75, 1879 (1995); D. Bear, et al. Phys. Rev. Lett. 85 (2000) 5038 [Errat. 89 (2002) 209902]

View on Pith 1994

[10] [10]

E.G. Adelberger et al. , in Physics Beyond the Stan- dard Model, 1998, Santa Fe (World Scientiﬁc, Singapore, 1999); M.G. Harris, PhD Thesis, University of Washing- ton, 1998; B.R. Heckel et al. , in Proceedings of the In- ternational Conference on Orbis Scientiae, 1999, Coral Gables (Kluwer, New York, 2000)

View on Pith 1998

[11] [11]

R. Gambini and J. Pullin, Phys. Rev. D59 (1999) 124021; J. Alfaro, H.A. Morales-Tecotl and L.F. Urrutia, Phys. Rev. D65 (2002) 103509

View on Pith 1999

[12] [12]

J. Alfaro, H.A. Morales-Tecotl and L.F. Urrutia, hep- th/0208192

View on Pith

[13] [13]

H. Sahlmann and T. Thiemann, gr-qc/0207030; gr- qc/0207031. 4

View on Pith Pith review arXiv