Canonical Quantization of Singular Configuration Spaces: Symmetry Reduction, Mass Gap Bounds, and Non-smooth Calculus

Singular configuration spaces require extensions of the usual operators and dynamics of quantum mechanics. Using metric-measure calculus, this work constructs states, observables and unitary evolution under suitable assumptions. A curvature-based technique bounds spectral gaps after symmetry reduction. Examples include a constrained oscillator, lattice Yang–Mills theory and fractional-dimensional spaces; the talk also considers prospective connections with the Yang–Mills mass-gap problem and gravity.