Checking the S matrix in QCD in axial gauges within the generalized Leibbrandt-Mandelstam prescription

Journal Article · Fri Sep 15 04:00:00 EDT 1989 · Physical Review (Section) D: Particles and Fields; (USA)

DOI:https://doi.org/10.1103/PhysRevD.40.2027· OSTI ID:5506261

Pollak, G ^[1]

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1. Institut fur Theoretische Physik, Technische Universitat Wien, Wiedner Hauptstrasse 8-10, A-1040 Wien, Austria (AT)

We apply the Leibbrandt-Mandelstam prescription to QCD within a family of gauges comprising the homogeneous axial gauge and the planar gauge. We calculate to one-loop order the UV-divergent parts of the quark self-energy, the quark-quark-gluon vertex, and the four-quark one-particle-irreducible vertex. The results are found to satisfy the Slavnov-Taylor-Lee identity. Summing up the contributions to the {ital S}-matrix element for quark-quark scattering, we show that the result is indeed independent of the gauge parameters {ital n}{sub {mu}} and {alpha} and of the auxiliary vector {ital n}{sub {mu}}{sup *}. The nonlocal counterterms persisting in Green's functions for {ital n}{sup 2}{ne}0 are thus compatible with gauge independence of physical quantities. The Lorentz-noninvariant divergent structures (local as well as nonlocal ones) turn out to be proportional to the classical equations of motion.

• OSTI ID: 5506261
• Journal Information: Physical Review (Section) D: Particles and Fields; (USA), Journal Name: Physical Review (Section) D: Particles and Fields; (USA) Vol. 40:6; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

645204 -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- Strong Interactions & Properties
645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
ELEMENTARY PARTICLES
ENERGY
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GLUONS
GREEN FUNCTION
INTERACTIONS
INVARIANCE PRINCIPLES
LIGHT CONE
MATRICES
MATRIX ELEMENTS
PARTICLE INTERACTIONS
POSTULATED PARTICLES
PROPAGATOR
QUANTUM CHROMODYNAMICS
QUANTUM FIELD THEORY
QUARK-QUARK INTERACTIONS
RENORMALIZATION
S MATRIX
SCATTERING
SELF-ENERGY
SPACE-TIME
ULTRAVIOLET DIVERGENCES
VERTEX FUNCTIONS
WILSON LOOP
YANG-MILLS THEORY