A Unified Scheme for Generalized Sectors based on Selection Criteria. II. Spontaneously broken symmetries and some basic notions in quantum measurements

Abstract

Continuing the analysis in a unified scheme for treating generalized superselection sectors based upon the notion of selection criteria for states of relevance in quantum physics, we extend the Doplicher-Roberts superselection theory for recovering the field algebra and the gauge group (of the first kind) from the data of group invariant observables to the situations with spontaneous symmetry breakdown: in use of the machinery proposed, the basic structural features of the theory with spontaneously broken symmetry, are clarified in a clear-cut way, such as the degenerate vacua parametrized by the variable belonging to the relevant homogeneous space, the Goldstone modes and condensates.