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arXiv:quant-ph/9706040 · Journal of Mathematical Physics

Quantization of a particle in a background Yang–Mills field

Yihren Wu

Published Feb 1, 1998• 10 citations
arXivHTMLPDF

Abstract

Two classes of observables defined on the phase space of a particle are quantized, and the effects of the Yang–Mills field are discussed in the context of geometric quantization.
DOI
10.1063/1.532357

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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. (orig.)