Propagator DysonSchwinger equations of Coulomb gauge YangMills theory within the first order formalism
Abstract
Coulomb gauge YangMills theory within the first order formalism is considered with a view of deriving the propagator DysonSchwinger equations. The first order formalism is studied with special emphasis on the BecchiRouetStora (BRS) invariance and it is found that there exists two forms of invarianceinvariance 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 WardTakahashi 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 twopoint Green's functions are derived. The propagator DysonSchwinger equations are derived and certain aspects (energy independence of ghost Green's functions and the cancellation of energy divergences) are discussed.
 Authors:
 Institut fuer Theoretische Physik, Universitaet Tuebingen, Auf der Morgenstelle 14, D72076 Tuebingen (Germany)
 Publication Date:
 OSTI Identifier:
 21011114
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.045021; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COULOMB FIELD; EQUATIONS OF MOTION; FIELD EQUATIONS; GREEN FUNCTION; PROPAGATOR; QUANTUM FIELD THEORY; SCHWINGER FUNCTIONAL EQUATIONS; SYMMETRY; YANGMILLS THEORY
Citation Formats
Watson, P., and Reinhardt, H. Propagator DysonSchwinger equations of Coulomb gauge YangMills theory within the first order formalism. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.045021.
Watson, P., & Reinhardt, H. Propagator DysonSchwinger equations of Coulomb gauge YangMills theory within the first order formalism. United States. doi:10.1103/PHYSREVD.75.045021.
Watson, P., and Reinhardt, H. Thu .
"Propagator DysonSchwinger equations of Coulomb gauge YangMills theory within the first order formalism". United States.
doi:10.1103/PHYSREVD.75.045021.
@article{osti_21011114,
title = {Propagator DysonSchwinger equations of Coulomb gauge YangMills theory within the first order formalism},
author = {Watson, P. and Reinhardt, H.},
abstractNote = {Coulomb gauge YangMills theory within the first order formalism is considered with a view of deriving the propagator DysonSchwinger equations. The first order formalism is studied with special emphasis on the BecchiRouetStora (BRS) invariance and it is found that there exists two forms of invarianceinvariance 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 WardTakahashi 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 twopoint Green's functions are derived. The propagator DysonSchwinger equations are derived and certain aspects (energy independence of ghost Green's functions and the cancellation of energy divergences) are discussed.},
doi = {10.1103/PHYSREVD.75.045021},
journal = {Physical Review. D, Particles Fields},
number = 4,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

Perturbative Coulomb gauge YangMills theory within the first order formalism is considered. Using a differential equation technique and dimensional regularization, analytic results for both the ultraviolet divergent and finite parts of the twopoint functions at oneloop order are derived. It is shown how the nonultraviolet divergent parts of the results are finite at spacelike momenta with kinematical singularities on the lightcone and subsequent branch cuts extending into the timelike region.

DysonSchwinger Equations and Coulomb Gauge YangMills Theory
Coulomb gauge YangMills theory is considered within the first order formalism. It is shown that the action is invariant under both the standard BRS transform and an additional component. The WardTakahashi identity arising from this nonstandard transform is shown to be automatically satisfied by the equations of motion. 
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Simple model systems like the O(N) sigma model, the GrossNeveu model, and the random matrix model are solved at N..>..infinity using DysonSchwinger equations and the fact that the HartreeFock approximation is exact at N..>..infinity. The complete string equations of the U(infinity) lattice gauge theory are presented. These must include both string rearrangement and splitting. Comparison is made with the ''continuum'' equations of Makeenko and Migdal which are structurally different. The difference is ascribed to inequivalent regularization procedures in the treatment of string splitting or rearrangement at intersections. 
Confining solution of the DysonSchwinger equations in Coulomb gauge
The DysonSchwinger equations arising from minimizing the vacuum energy density in the Hamiltonian approach to YangMills theory in Coulomb gauge are solved numerically. A new solution is presented which gives rise to a strictly linearly rising static quark potential and whose existence was previously observed in the infrared analysis of the DysonSchwinger equations. For the new solution we also present the static quark potential and calculate the running coupling constant from the ghostgluon vertex.