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.
Remarks on the Formulation of Quantum Mechanics with Classical Pictures and on Relations between Linear Scalar Fields and Hydrodynamical Fields
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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.