U(1) Gauge Theory as Quantum Hydrodynamics

Details U(1) Gauge Theory as Quantum Hydrodynamics U(1) Gauge Theory as Quantum Hydrodynamics

2002-10-30

arxiv.org/abs/cond-mat/0210673v3

Pramana62:101-114,2004

Physics

Condensed Matter

Other Condensed Matter

15 pages, Plain LaTeX, final published version

Scientific paper

10.1007/BF02704430

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.

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