Quantum Indeterminacy, Gauge Symmetries and Symplectic Reduction

Gabriel Catren (1)

1 SPHERE (UMR_7219) - Sciences, Philosophie, Histoire

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.

Mots clés: Quantum Mechanics; Gauge Symmetries

Domaines: Histoire, Philosophie et Sociologie des sciences

Gabriel Catren. Quantum Indeterminacy, Gauge Symmetries and Symplectic Reduction. Frontiers of Fundamental Physics 14, Jul 2014, Marseille, France. ⟨halshs-01527010⟩