Quantum Mechanics as a Gauge Theory of Metaplectic Spinor Fields

TL;DR

This paper reveals a hidden gauge theory structure in quantum mechanics, showing its equivalence to a Yang-Mills theory with an infinite-dimensional gauge group over symplectic manifolds, offering a new geometric perspective.

Contribution

It introduces a gauge-theoretic reformulation of quantum mechanics using metaplectic spinor fields and local Hilbert spaces, providing a novel geometric and group-theoretical framework.

Findings

Quantum mechanics is equivalent to a Yang-Mills theory with an infinite-dimensional gauge group.

States and observables are represented as local spinor fields transforming under the metaplectic group.

A new background-quantum split symmetry is identified as central to the formulation.

Abstract

A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a nondynamical connection. It is defined over an arbitrary symplectic manifold which constitutes the phase-space of the system under consideration. The ''matter fields'' are local generalizations of states and observables; they assume values in a family of local Hilbert spaces (and their tensor products) which are attached to the points of phase-space. Under local frame rotations they transform in the spinor representation of the metaplectic group Mp(2N), the double covering of Sp(2N). The rules of canonical quantization are replaced by two independent postulates with a simple group theoretical and differential geometrical interpretation. A novel background-quantum split symmetry plays a central role.