Time-independent stochastic quantization, Dyson-Schwinger equations, and infrared critical exponents in QCD

Daniel Zwanziger
Phys. Rev. D 67, 105001 – Published 2 May 2003
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Abstract

We derive the equations of time-independent stochastic quantization, without reference to an unphysical fifth time, from the principle of gauge equivalence. It asserts that probability distributions P that give the same expectation values for gauge-invariant observables W=dAWP are physically indistinguishable. This method escapes the Gribov critique. We derive an exact system of equations that closely resembles the Dyson-Schwinger equations of Faddeev-Popov theory. The system is truncated and solved nonperturbatively, by means of a power law ansatz, for the critical exponents that characterize the asymptotic form at k0 of the gluon propagator in Landau gauge. For the transverse and longitudinal parts, we find, respectively, DT(k2)1αT(k2)0.043, suppressed and in fact vanishing, though weakly, and DLa(k2)1αLa(k2)1.521, enhanced, with αT=2αL. Although the longitudinal part vanishes with the gauge parameter a in the Landau-gauge limit a0 there are vertices of order a1 so, counterintuitively, the longitudinal part of the gluon propagator does contribute in internal lines in the Landau gauge, replacing the ghost that occurs in Faddeev-Popov theory. We compare our results with the corresponding results in Faddeev-Popov theory.

  • Received 14 June 2002

DOI:https://doi.org/10.1103/PhysRevD.67.105001

©2003 American Physical Society

Authors & Affiliations

Daniel Zwanziger*

  • Physics Department, New York University, New York, New York 10003

  • *Email address: Daniel.Zwanziger@nyu.edu

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Vol. 67, Iss. 10 — 15 May 2003

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