Yang-Mills theory on a momentum lattice: Gauge invariance, chiral invariance, and no fermion doubling

Journal Article · Fri Feb 15 00:00:00 EST 1991 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.43.1385· OSTI ID:5697732

Berube, D; Kroeger, H; Lafrance, R; Marleau, L ^[1]

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1. Departement de Physique, Universite Laval, Quebec, Province de Quebec, G1K 7P4 Canada (CA)

We discuss properties of a noncompact formulation of gauge theories with fermions on a momentum ({ital k}) lattice. (a) This formulation is suitable to build in Fourier acceleration in a direct way. (b) The numerical effort to compute the action (by fast Fourier transform) goes essentially like log{ital V} with the lattice volume {ital V}. (c) For the Yang-Mills theory we find that the action conserves gauge symmetry and chiral symmetry in a weak sense: On a finite lattice the action is invariant under infinitesimal transformations with compact support. Under finite transformations these symmetries are approximately conserved and they are restored on an infinite lattice and in the continuum limit. Moreover, these symmetries also hold on a finite lattice under finite transformations, if the classical fields, instead of being {ital c}-number valued, take values from a finite Galois field. (d) There is no fermion doubling. (e) For the {phi}{sup 4} model we investigate the transition towards the continuum limit in lattice perturbation theory up to second order. We compute the two- and four-point functions and find local and Lorentz-invariant results. (f) In QED we compute a one-loop vacuum polarization and find in the continuum limit the standard result. (g) As a numerical application, we compute the propagator {l angle}{phi}({ital k}){phi}({ital k}{prime}){r angle} in the {phi}{sup 4} model, investigate Euclidean invariance, and extract {ital m}{sub {ital R}} as well as {ital Z}{sub {ital R}}. Moreover we compute {l angle}{ital F}{sub {mu}{nu}}({ital k}){ital F}{sub {mu}{nu}}({ital k}{prime}){r angle} in the SU(2) model.

• OSTI ID: 5697732
• Journal Information: Physical Review, D (Particles Fields); (USA), Vol. 43:4; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
YANG-MILLS THEORY
GAUGE INVARIANCE
CHIRAL SYMMETRY
EUCLIDEAN SPACE
FERMIONS
FOURIER TRANSFORMATION
LATTICE FIELD THEORY
LORENTZ INVARIANCE
PERTURBATION THEORY
PHI4-FIELD THEORY
PROPAGATOR
QUANTUM ELECTRODYNAMICS
SPACE-TIME
SU-2 GROUPS
U-1 GROUPS
VACUUM POLARIZATION
ELECTRODYNAMICS
FIELD THEORIES
INTEGRAL TRANSFORMATIONS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL SPACE
QUANTUM FIELD THEORY
RIEMANN SPACE
SPACE
SU GROUPS
SYMMETRY
SYMMETRY GROUPS
TRANSFORMATIONS
U GROUPS
645400* - High Energy Physics- Field Theory
645300 - High Energy Physics- Particle Invariance Principles & Symmetries