Symmetries,quantum Geometry, and the Fundamental Interactions

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. Paper presented at the XXIII International Colloquium on Group Theoretical Methods in Physics, Dubna, Russia, 30 July 05 August, 2000, quant-ph/0012011.