On the Structure of Physical Measures in Gauge Theories

TL;DR

This paper critically examines the standard method of defining physical measures in gauge theories, revealing contradictions with models like confinement within the rigorous Ashtekar framework.

Contribution

It demonstrates that the common exponential action-based measure definition conflicts with key physical properties in certain gauge theories, especially those with confinement.

Findings

Standard measure definitions are incompatible with confinement models.

The results are rigorously established within the Ashtekar approach.

Highlights limitations of traditional measure constructions in gauge theories.

Abstract

It is indicated that the definition of physical measures via ``exponential of minus the action times kinematical measure'' contradicts properties of certain physical models. In particular, theories describing confinement typically cannot be gained this way. The results are rigorous within the Ashtekar approach to gauge field theories.