Schrödinger equation is locally equivalent to a non-relativistic gauge theory via one-form or two-form gauge fields on the probability current, with global topology from phase winding quantization.
Holonomy and vortex structures in quantum hydrodynamics
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The Schrodinger Equation as a Gauge Theory
Schrödinger equation is locally equivalent to a non-relativistic gauge theory via one-form or two-form gauge fields on the probability current, with global topology from phase winding quantization.