Symmetries, Quantum Geometry, and the Fundamental Interactions

Abstract

A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making these relations dynamical implies the non local effect of the fundamental interactions on the wave function, as in the Aharonov-Bohm effect and its generalizations to non Abelian gauge fields and gravity. The usual space-time geometry is obtained as the classical limit of this quantum geometry using the quantum state space metric.