Schr\"odinger Functional and Quantization of Gauge Theories in the Temporal Gauge

TL;DR

This paper discusses the quantization of gauge theories using the Schr"odinger Functional in the temporal gauge, highlighting its advantages and the treatment of external color sources within this formalism.

Contribution

It provides a concise formulation of the Schr"odinger Functional in the temporal gauge, including the handling of external color sources and the automatic implementation of Gauss' law.

Findings

Temporal gauge simplifies gauge fixing in path integrals.

Gauss' law is automatically enforced in the formalism.

External color sources are incorporated into the Schr"odinger Functional.

Abstract

In the language of Feynman path integrals the quantization of gauge theories is most easily carried out with the help of the Schr\"odinger Functional (SF). Within this formalism the essentially unique gauge fixing condition is $A_{\circ} = 0$ (temporal gauge), as any other rotationally invariant gauge choice can be shown to be functionally equivalent to the former. In the temporal gauge Gauss' law is automatically implemented as a constraint on the states. States not annihilated by the Gauss operator describe the situation in which external (infinitely heavy) colour sources interact with the gauge field. The SF in the presence of an arbitrary distribution of external colour sources can be expressed in an elegant and concise way.