2015/02/23 by Franco Strocchi, Strocchi, Franco
Physics and Astronomy · #81P05 #81R40 #81T13 #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #History and Philosophy of Physics (physics.hist-ph) #Particle physics theoretical and experimental studies #Quantum Mechanics and Applications #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1502.06540
openalex publication_date 2015/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables \em and the (physical) states. For infinitely extended systems the states fall into physically disjoint \em phases characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field theories. The topological invariants of a local gauge group define superselected quantum numbers, which account for the θ vacua.