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

Journal Article · Fri Sep 15 00:00:00 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), Vol. 40:6; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM CHROMODYNAMICS
S MATRIX
GAUGE INVARIANCE
GLUONS
GREEN FUNCTION
LIGHT CONE
MATRIX ELEMENTS
PROPAGATOR
QUARK-QUARK INTERACTIONS
RENORMALIZATION
SCATTERING
SELF-ENERGY
ULTRAVIOLET DIVERGENCES
VERTEX FUNCTIONS
WILSON LOOP
YANG-MILLS THEORY
BOSONS
ELEMENTARY PARTICLES
ENERGY
FIELD THEORIES
FUNCTIONS
INTERACTIONS
INVARIANCE PRINCIPLES
MATRICES
PARTICLE INTERACTIONS
POSTULATED PARTICLES
QUANTUM FIELD THEORY
SPACE-TIME
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