Spectral Function Sum Rule for Gauge Fields

Abstract

An exact evaluation of the wave function renormalization constant for the color gauge field is carried out because of the close relationship that it bears to color confinement. Since this constant can be expressed as an integral of the absorptive part or the spectral function of the gauge field propagator, the result takes the form of a sum rule for the spectral function. It should be emphasized that asymptotic freedom plays an essential role in its derivation.

Renormalization constant of the color gauge field as a probe of confinement

“…is realized. It so happens that Z 3 can be evaluated exactly in QCD and we can readily check the CCC [28,32], but before entering this subject we have to discuss a more fundamental subject.…”

“…Bearing this in mind we introduce the concept of the equivalence class of gauges [28,32]. Let us consider a class of Lagrangian densities {L α } representing a gauge theory such as QCD.…”

“…Evaluation of α ∞ has been published elsewhere [17,28,32] so that we shall be brief in what follows.…”

Gauge dependence of Green’s functions in QCD and QED

“…In Section 4 the RG equations for the running coupling constant and gauge parameter are solved and their ultra-violet asymptotic limits are studied to answer the question of gauge-dependence of Green's functions. For this purpose we derive a sum rule [5,6] which enables us to express the renormalization constant Z −1 3 in a simple form. Green's functions defined as the vacuum expectation values of the time-ordered products of BRS invariant operators are always independent of α, but those made up of BRS variant ones are α-dependent.…”

Renormalization Constants in Quantum Chromodynamics

“…1 The RC of the color gauge field Z 3 satisfies an identity, which is referred to as a sum rule, and is given by…”