Non-perturbative modification of the Faddeev-Popov formula

Daniel Zwanziger

doi:10.1016/0370-2693(82)90357-4

Non-perturbative modification of the Faddeev-Popov formula

Daniel Zwanziger

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	337-339
Number of pages	3
Journal	Physics Letters B
Volume	114
Issue number	5
DOIs	https://doi.org/10.1016/0370-2693(82)90357-4
State	Published - Aug 5 1982

ASJC Scopus subject areas

Nuclear and High Energy Physics

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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.",

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AB - 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.

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