One-loop analytic computation of the energy-momentum tensor for lattice gauge theories

Caracciolo, Sergio; Menotti, Pietro; Pelissetto, Andrea

doi:10.1016/0550-3213(92)90339-d

Cited by 63 publications

(99 citation statements)

References 22 publications

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“…[2,3]. The strategy is quite analogous to the one for the chiral symmetry on the lattice studied in Ref.…”

Section: Emt With the Lattice Regularizationmentioning

confidence: 88%

“…2 With the dimensional regularization, T µν will be finite even without such a subtraction; here we define the renormalized EMT by subtracting VEV to make expressions be consistent also with the lattice regularization. 3 It is interesting to note that a computation of the trace anomaly of the Wilson fermion in a pioneering work [5] yielded −15 times the conventional trace anomaly. Later, it was realized in Ref.…”

Section: Emt With the Lattice Regularizationmentioning

confidence: 99%

“…[4]. 3 We start with a possible definition of a "would-be infinitesimal translation" on the link variables U(x, µ). Since the infinitesimal translation is in any case broken by the lattice structure, the definition is to a large extent arbitrary.…”

Section: Emt With the Lattice Regularizationmentioning

confidence: 99%

“…In this expression, the naive lattice transcription of the classical EMTT naive µν (x) is defined bŷ T naive µν (x) ≡T [6] µν (x) +T [3] µν (x) (3.3)…”

Section: Pos(lattice2016)002mentioning

confidence: 99%

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Energy-momentum tensor on the lattice: recent developments

Suzuki

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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“…[2,3]. The strategy is quite analogous to the one for the chiral symmetry on the lattice studied in Ref.…”

Section: Emt With the Lattice Regularizationmentioning

confidence: 88%

Section: Emt With the Lattice Regularizationmentioning

confidence: 99%

Section: Emt With the Lattice Regularizationmentioning

confidence: 99%

“…In this expression, the naive lattice transcription of the classical EMTT naive µν (x) is defined bŷ T naive µν (x) ≡T [6] µν (x) +T [3] µν (x) (3.3)…”

Section: Pos(lattice2016)002mentioning

confidence: 99%

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Energy-momentum tensor on the lattice: recent developments

Suzuki

2017

Proceedings of 34th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2016)

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“…In [1] we presented a general technique which allows to express every one-loop bosonic integral at zero external momentum in terms of two unknown basic quantities which could be computed numerically with high precision. This method allows the complete evaluation of every diagram with gluon propagators.…”

mentioning

confidence: 99%

How to compute one-loop Feynman diagrams in lattice QCD with Wilson fermions

Burgio

Caracciolo

Pelissetto

1997

Nuclear Physics B - Proceedings Supplements

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We describe an algebraic algorithm which allows to express every one-loop lattice integral with gluon or Wilsonfermion propagators in terms of a small number of basic constants which can be computed with arbitrary high precision. Although the presentation is restricted to four dimensions the technique can be generalized to every space dimension. We also give a method to express the lattice free propagator for Wilson fermions in coordinate space as a linear function of its values in eight points near the origin. This is an essential step in order to apply the recent methods of Lüscher and Weisz to higher-loop integrals with fermions.In [1] we presented a general technique which allows to express every one-loop bosonic integral at zero external momentum in terms of two unknown basic quantities which could be computed numerically with high precision. This method allows the complete evaluation of every diagram with gluon propagators.We have recently generalized [2] this technique to deal with integrals with both gluonic and fermionic propagators. For the fermions we use the Wilson action [3]. Notice that our method depends only on the structure of the propagator and thus it can be applied in calculations with the standard Wilson action as well as with the improved clover action [4]. We show that every integral at zero external momentum can be expressed in terms of a small number of basic quantities (nine for purely fermionic integrals, fifteen for integrals with bosonic and fermionic propagators). The advantage of this procedure is twofold: first of all every Feynman diagram can be computed in a completely symbolic way making it easier to perform checks and verify cancellations; moreover the basic constants can be easily computed with high precision and thus the numerical error on the final result can be reduced at will. Although the presentation is restricted to * Speaker at the conference.four dimensions the technique can be generalized to every space dimension. Definewhere n i are positive integers, p and q are arbitrary integers (not necessarily positive),is the denominator appearing in the propagator for Wilson fermions 2 . In the following when one2 To be precise, D F (k, m f ) is the denominator in the propagator for Wilson fermions only for m f = 0. For m f = 0 the correct denominator would bêHowever in our discussion m f will only play the role of an infrared regulator and thus it does not need to be the true fermion mass. The definition (3) is easier to handle than (4).

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Non-perturbative definition of the QCD energy-momentum tensor on the lattice

Brida

Giusti

2020

J. High Energ. Phys.

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We present a strategy to define non-perturbatively the energy-momentum tensor in Quantum Chromodynamics (QCD) which satisfies the appropriate Ward identities and has the right trace anomaly. The tensor is defined by regularizing the theory on a lattice, and by fixing its renormalization constants non-perturbatively by suitable Ward identities associated to the Poincaré invariance of the continuum theory. The latter are derived in thermal QCD with a non-zero imaginary chemical potential formulated in a moving reference frame. A renormalization group analysis leads to simple renormalizationgroup-invariant definitions of the gluonic and fermionic contributions to either the singlet or the non-singlet components of the tensor, and therefore of their form factors among physical states. The lattice discussion focuses on the Wilson discretization of quark fields but the strategy is general. Specific to that case, we also carry out the analysis for the on-shell O(a)-improvement of the energy-momentum tensor. The renormalization and improvement programs profit from the fact that, as shown here, the thermal theory enjoys de-facto automatic O(a)-improvement at finite temperature. The validity of the proposal is scrutinized analytically by a study to 1-loop order in lattice perturbation theory with shifted and twisted (for quarks only) boundary conditions. The latter provides also additional useful insight for a precise non-perturbative calculation of the renormalization constants. The strategy proposed here is accessible to Monte Carlo computations, and in this sense it provides a practical way to define non-perturbatively the energy-momentum tensor in QCD.

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One-loop analytic computation of the energy-momentum tensor for lattice gauge theories

Cited by 63 publications

References 22 publications

Energy-momentum tensor on the lattice: recent developments

Energy-momentum tensor on the lattice: recent developments

How to compute one-loop Feynman diagrams in lattice QCD with Wilson fermions

Non-perturbative definition of the QCD energy-momentum tensor on the lattice

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