Gauge equivalence in QCD: The Weyl and Coulomb gauges

Kurt Haller and Hai-cang Ren
Phys. Rev. D 68, 085002 – Published 7 October 2003
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Abstract

The Weyl-gauge (A0a=0) QCD Hamiltonian is unitarily transformed to a representation in which it is expressed entirely in terms of gauge-invariant quark and gluon fields. In a subspace of gauge-invariant states we have constructed that implement the non-Abelian Gauss’s law, this unitarily transformed Weyl-gauge Hamiltonian can be further transformed and, under appropriate circumstances, can be identified with the QCD Hamiltonian in the Coulomb gauge. We demonstrate an isomorphism that materially facilitates the application of this Hamiltonian to a variety of physical processes, including the evaluation of S-matrix elements. This isomorphism relates the gauge-invariant representation of the Hamiltonian and the required set of gauge-invariant states to a Hamiltonian of the same functional form but dependent on ordinary unconstrained Weyl-gauge fields operating within a space of “standard” perturbative states. The fact that the gauge-invariant chromoelectric field is not Hermitian has important implications for the functional form of the Hamiltonian finally obtained. When this non-Hermiticity is taken into account, the “extra” vertices in the Christ-Lee’ Coulomb-gauge Hamiltonian are natural outgrowths of the formalism. When this non-Hermiticity is neglected, the Hamiltonian used in the earlier work of Gribov and others results.

  • Received 3 October 2002

DOI:https://doi.org/10.1103/PhysRevD.68.085002

©2003 American Physical Society

Authors & Affiliations

Kurt Haller*

  • Department of Physics, University of Connecticut, Storrs, Connecticut 06269-3046, USA

Hai-cang Ren

  • Physics Department, The Rockefeller University, 1230 York Avenue, New York, New York 10021-6399, USA

  • *Email: Kurt.Haller@uconn.edu

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Vol. 68, Iss. 8 — 15 October 2003

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