A Manifestly Gauge-Invariant Approach to Quantum Theories of Gauge Fields

TL;DR

This paper discusses the challenges of formulating quantum gauge theories due to the non-linear space of histories and proposes a new approach to address these gauge invariance issues.

Contribution

It introduces a manifestly gauge-invariant framework for quantum gauge theories, extending the standard constructive quantum field theory to handle non-linearities.

Findings

Identifies the intrinsic non-linearity of the space of histories in gauge theories.

Proposes a new approach to maintain gauge invariance in quantum formulations.

Provides a pedagogical overview of the problem and a potential resolution avenue.

Abstract

In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be extended to face these {\it kinematical} non-linearities squarely. We first present a pedagogical account of this problem and then suggest an avenue for its resolution.