Propagator Dyson-Schwinger equations of Coulomb gauge Yang-Mills theory within the first order formalism

Journal Article · Thu Feb 15 04:00:00 EST 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.75.045021· OSTI ID:21011114

Watson, P; Reinhardt, H ^[1]

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1. Institut fuer Theoretische Physik, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany)

Coulomb gauge Yang-Mills theory within the first order formalism is considered with a view of deriving the propagator Dyson-Schwinger equations. The first order formalism is studied with special emphasis on the Becchi-Rouet-Stora (BRS) invariance and it is found that there exists two forms of invariance--invariance under the standard BRS transform and under a second, nonstandard transform. The field equations of motion and symmetries are derived explicitly and certain exact relations that simplify the formalism are presented. It is shown that the Ward-Takahashi identity arising from invariance under the nonstandard part of the BRS transform is guaranteed by the functional equations of motion. The Feynman rules and the general decomposition of the two-point Green's functions are derived. The propagator Dyson-Schwinger equations are derived and certain aspects (energy independence of ghost Green's functions and the cancellation of energy divergences) are discussed.

• OSTI ID: 21011114
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 75; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COULOMB FIELD
EQUATIONS OF MOTION
FIELD EQUATIONS
GREEN FUNCTION
PROPAGATOR
QUANTUM FIELD THEORY
SCHWINGER FUNCTIONAL EQUATIONS
SYMMETRY
YANG-MILLS THEORY