U(1) Gauge theory as quantum hydrodynamics

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.

Bosonization and quantum hydrodynamics

“…This is bound to lead to the conclusion that the system is a Luttinger liquid with a characteristic exponent, a result that will be more easily and elegantly shown using sea-bosons later on in this article. The current and density correlations may be conveniently calculated [at least at the RPA (random phase approximation) level for translationally invariant systems] using the Lagrangian approach that is conducive to the introduction of gauge fields [10]. To this end we derive an action functional for the free electron system in terms of the hydrodynamic variables in any number of dimensions at the RPA level using the sea-boson formalism.…”