Superselection Principle and Pure States of n-Identical Particles

Abstract

Wightman's assumption of commutative superselection rules is proved to be equivalent to Jauch's assumption of existence of a complete set of commuting observables. The analysis of coherence is carried out by using the Gel'fand representation theory and the general structure of the complete sets of compatible observables is given when the Hilbert space is separable. The above equivalence provides the physical grounds to incorporate both assumptions into the axiomatic foundations of quantum theory as a single ``superselection principle.'' To illustrate how this principle works, the problem of determining the physically realizable states of an assembly of n‐identical particles is analyzed and solved.