Quantum Indeterminacy, Gauge Symmetries and Symplectic Reduction

International audienceAs 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