Phase Spaces and Operator Algebras for Subregions in Gauge Theory and Quantum Gravity

Gravitational subregions cannot be specified independently of gauge symmetry and boundary degrees of freedom. This seminar connects extended phase spaces with crossed-product operator algebras to address difficulties with symmetry generators, factorization and entanglement entropy. It recovers a semiclassical construction and explores possible nonperturbative extensions involving fuzzy subregions, quantum reference frames and generalized entropy.