U(1) Gauge Theory as Quantum Hydrodynamics

TL;DR

This paper reformulates U(1) gauge theories as quantum hydrodynamics using a polar decomposition, deriving exact formulas for condensate fraction, anomalous exponent, and vortex strength without gauge fixing.

Contribution

It introduces a polar decomposition approach to gauge theories, providing exact formulas for key physical quantities and avoiding gauge fixing.

Findings

Derived an exact formula for the condensate fraction.

Provided an exact formula for the anomalous exponent when condensate is zero.

Computed vortex strength involving radiation corrections.

Abstract

It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The path integral approach is used to compute the partition function. When gauge fields are included, the constraint brought about by gauge invariance simply means an appropriate linear combination of the gradients of the phase variable and the gauge field is invariant. No gauge fixing is needed in this approach that is closest to the spirit of the gauge principle. We derive an exact formula for the condensate fraction and in case it is zero, an exact formula for the anomalous exponent. We also derive a formula for the vortex strength which involves computing radiation corrections.