Gauge-invariant fields in the temporal gauge, Coulomb-gauge fields, and the Gribov ambiguity

Details Gauge-invariant fields in the temporal gauge, Coulomb-gauge fields, and the Gribov ambiguity Gauge-invariant fields in the temporal gauge, Coulomb-gauge fields, and the Gribov ambiguity

2000-04-28

arxiv.org/abs/hep-th/0004205v4

Int.J.Mod.Phys. A16 (2001) 2789

Physics

High Energy Physics

High Energy Physics - Theory

27 pages, 1 figure; text has been revised and references added

Scientific paper

10.1142/S0217751X01004311

We examine the relation between Coulomb-gauge fields and the gauge-invariant fields constructed in the temporal gauge for two-color QCD by comparing a variety of properties, including their equal-time commutation rules and those of their conjugate chromoelectric fields. We also express the temporal-gauge Hamiltonian in terms of gauge-invariant fields and show that it can be interpreted as a sum of the Coulomb-gauge Hamiltonian and another part that is important for determining the equations of motion of temporal-gauge fields, but that can never affect the time evolution of ``physical'' state vectors. We also discuss multiplicities of gauge-invariant temporal-gauge fields that belong to different topological sectors and that, in previous work, were shown to be based on the same underlying gauge-dependent temporal-gauge fields. We argue that these multiplicities of gauge-invariant fields are manifestations of the Gribov ambiguity. We show that the differential equation that bases the multiplicities of gauge-invariant fields on their underlying gauge-dependent temporal-gauge fields has nonlinearities identical to those of the ``Gribov'' equation, which demonstrates the non-uniqueness of Coulomb-gauge fields. These multiplicities of gauge-invariant fields --- and, hence, Gribov copies --- appear in the temporal gauge, but only with the imposition of Gauss's law and the implementation of gauge invariance; they do not arise when the theory is represented in terms of gauge-dependent fields and Gauss's law is left unimplemented.

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