Quantum Indeterminacy, Gauge Symmetries and Symplectic Reduction

Abstract

As a consequence of Heisenberg indeterminacy principle, quantum states are defined by half the number of variables required in classical mechanics. The main claim of this paper is that this reduction in the number of variables required to completely describe a physical system can be understood as a consequence of the same formalism underlying the reduction procedure used in gauge theories, namely the Mardsen-Weinstein symplectic reduction. This fact points towards a gauge-theoretical interpretation of the indeterminacy principle in quantum mechanics.