GAUGE-INVARIANT RENORMALIZABILITY OF NON-ABELIAN STOCHASTICALLY QUANTIZED THEORIES

Abstract

The generating functional of a stochastically quantized non-Abelian theory is formulated in a gauge-invariant form in the nonequilibrium phase in (D + 1) dimensions. In the gauge [Formula: see text], μ = 1, … D, in the case of dimensional regularization, this formulation is shown to be completely equivalent (in perturbation theory) to the usual stochastic quantization with an addition to the Langevin equation of the Zwanziger type term [Formula: see text] for a rather wide class of functionals υ (A). In dimensional regularization, the determinant due to ghost fields is equal to unity in perturbation theory but has Gribov's zeros in nonperturbative calculations. The effective action in a generating functional possesses BRST-symmetry from which one can derive Ward-Fradkin-Takahashi-Slavnov-Taylor identities (WI) that provide the connections between the renormalization constants of vertices and fields and the gauge-invariant renormalizability of the theory in nonequilibrium and equilibrium phases for D ≤ 4. The renormalization constants of fields and parameters are calculated in dimensional regularization in the one-loop approximation; it is shown that due to the nontrivial renormalization of the kinetic coefficient in nonequilibrium phase, the β functions turn out to be distinct in these phases, in four dimensions the β function coinciding with the ordinary one in equilibrium phase. Fulfillment of the principal WI in perturbation theory is checked.