The Schrödinger equation is locally equivalent to a gauge theory with one-form fields in 2+1D and two-form fields in 3+1D, with BF and Chern-Simons terms organizing electromagnetic couplings, anyons, Berry phases, and infrared structures.
The geometro-hydrodynamical formalism of the quantum spinning particle
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The Schrodinger Equation as a Gauge Theory
The Schrödinger equation is locally equivalent to a gauge theory with one-form fields in 2+1D and two-form fields in 3+1D, with BF and Chern-Simons terms organizing electromagnetic couplings, anyons, Berry phases, and infrared structures.