Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge

Journal Article · Wed Apr 15 00:00:00 EDT 2009 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2008.09.005· OSTI ID:21167728

Reinhardt, H. ^[1]; Schleifenbaum, W. ^[2]

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1. Institut fuer Theoretische Physik, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany), E-mail: [e-mail]
2. Institut fuer Theoretische Physik, Universitaet Tuebingen, Auf der Morgenstelle 14, D-72076 Tuebingen (Germany), E-mail: [e-mail]

We study the Hamiltonian approach to 1 + 1 dimensional Yang-Mills theory in Coulomb gauge, considering both the pure Coulomb gauge and the gauge where in addition the remaining constant gauge field is restricted to the Cartan algebra. We evaluate the corresponding Faddeev-Popov determinants, resolve Gauss' law and derive the Hamiltonians, which differ in both gauges due to additional zero modes of the Faddeev-Popov kernel in the pure Coulomb gauge. By Gauss' law the zero modes of the Faddeev-Popov kernel constrain the physical wave functionals to zero colour charge states. We solve the Schroedinger equation in the pure Coulomb gauge and determine the vacuum wave functional. The gluon and ghost propagators and the static colour Coulomb potential are calculated in the first Gribov region as well as in the fundamental modular region, and Gribov copy effects are studied. We explicitly demonstrate that the Dyson-Schwinger equations do not specify the Gribov region while the propagators and vertices do depend on the Gribov region chosen. In this sense, the Dyson-Schwinger equations alone do not provide the full non-abelian quantum gauge theory, but subsidiary conditions must be required. Implications of Gribov copy effects for lattice calculations of the infrared behaviour of gauge-fixed propagators are discussed. We compute the ghost-gluon vertex and provide a sensible truncation of Dyson-Schwinger equations. Approximations of the variational approach to the 3 + 1 dimensional theory are checked by comparison to the 1 + 1 dimensional case.

• OSTI ID: 21167728
• Journal Information: Annals of Physics (New York), Vol. 324, Issue 4; Other Information: DOI: 10.1016/j.aop.2008.09.005; PII: S0003-4916(08)00140-1; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
APPROXIMATIONS
CHARGE STATES
COULOMB FIELD
DYSON REPRESENTATION
FOUR-DIMENSIONAL CALCULATIONS
FUNCTIONALS
GAUGE INVARIANCE
GLUONS
HAMILTONIANS
PROPAGATOR
SCHROEDINGER EQUATION
SCHWINGER FUNCTIONAL EQUATIONS
TWO-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS
YANG-MILLS THEORY