Quasilocal formulation of non-Abelian finite-element gauge theory

Journal Article · Wed May 01 04:00:00 EDT 1996 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.53.5898· OSTI ID:284027

Milton, K A ^[1]

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1. Department of Physics and Astronomy, The University of Oklahoma, Norman, Oklahoma 73019 (United States)

Recently it was shown how to formulate the finite-element equations of motion of a non-Abelian gauge theory, by gauging the free lattice difference equations, and simultaneously determining the form of the gauge transformations. In particular, the gauge-covariant field strength was explicitly constructed, locally, in terms of a path-ordered product of exponentials (link operators). On the other hand, the Dirac and Yang-Mills equations were nonlocal, involving sums over the entire prior lattice. Earlier, Matsuyama had proposed a local Dirac equation constructed from just the above-mentioned link operators. Here, we show how his scheme, which is closely related to our earlier one, can be implemented for a non-Abelian gauge theory. Although both Dirac and Yang-Mills equations are now local, the field strength is not. The technique is illustrated with a direct calculation of the current anomalies in two and four space-time dimensions. Unfortunately, unlike the original finite-element proposal, this scheme is in general nonunitary. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 284027
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 10 Vol. 53; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DIRAC EQUATION
EQUATIONS OF MOTION
GAUGE INVARIANCE
LATTICE FIELD THEORY
SPACE-TIME
UNIFIED GAUGE MODELS
YANG-MILLS THEORY