Global Gauge Group and Charge Carrying Fields

Abstract

In the traditional field theoretic approach (which in algebraic guise was summarized in III.1) we deal with a Hilbert space H^(u) which contains all superselection sectors as subspaces (the index u was added to indicate “universal”) and we deal with a larger algebra 𝔉 (denoted by 𝒜 in III.1) acting irreducibly on H^(u). It contains besides the observables also operators mapping from one coherent subspace to a different one (“charge carrying fields”). Furthermore there is a faithful, strongly continuous representation of a compact group, the global gauge group 𝒢, by unitary operators in ℬ(H^(u)), singling out the observables in 𝓕 as the invariant elements under the action induced by π^(u) (𝒢). In other words

$$\pi^{(u)}({\frak A})= {\frak F} \cap \pi^{(u)}({\cal G})^\prime.$$

(IV.4.1)