@article{bbf918d4bacd4b839a1d66ceb520442f,
title = "Non-perturbative modification of the Faddeev-Popov formula",
abstract = "A stochastic argument shows that the Faddeev-Popov formula in the Landau gauge may be modified by insertion of a factor χ(A) which is zero if A has a Gribov copy of smaller norm, ∫ d4 x A2, and is one otherwise. This provides a probability distribution P(A) which is positive P(A) {slanted equal to or greater-than} 0 and Lorentz invariant. The resulting distribution is concentrated on points where ∂ · D(A) has no negative eigenvalues. It is suggested that tr ln[∂ · D(A)/∂2] acts like an entropy which may shift the system to a non-perturbative phase.",
author = "Daniel Zwanziger",
note = "Funding Information: Here Scl \[A \] is the euclidean action of the field A. In a gauge theory we have Scl\[A\]= ~ 1 f d4x Zu,z,,a (F~v)2 where Fu~ = OuAa - OvA~ + fabeAbAe (the coupling --/.t --V constant g has been absorbed inA, and h =g2). In this case formula (2) cannot be used as it stands because Scl is gauge invariant, Scl \[Ag \] = Scl \[A\]w here Ag is a local gauge transform of A, so exp {-Scl \[A\]\]h} provides no convergence along gauge orbits and thus cannot be normalized. This difficulty is overcome by recalling that only gauge invariant objects are observable (~\[Ag\]= ~\[A\]s, o one may freely modify formula (2) by assigning an arbitrary distribution along each gauge orbit, provided the integral along the orbit is finite and the same for each orbit. Thus one arrives at distributions such as the Faddeev-Popov distribution \[1l * Research supported in part by the National Science Founda-tion Grant. No. PHY78-21503. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.",
year = "1982",
month = aug,
day = "5",
doi = "10.1016/0370-2693(82)90357-4",
language = "English (US)",
volume = "114",
pages = "337--339",
journal = "Physics Letters B",
issn = "0370-2693",
publisher = "Elsevier B.V.",
number = "5",
}