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 nonlocal 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.