Electronic Resource
Central decomposition of invariant states applications to the groups of time translations and of euclidean transformations in algebraic field theory
(1972)
Springer
ISSN:
14320916
Source:
Springer Online Journal Archives 18602000
Topics:
Mathematics
,
Physics
Notes:
Abstract With $$\mathfrak{A}$$ aC*algebra with unit andg∈G→α g a homomorphic map of a groupG into the automorphism group ofG, the central measureμ Φ of a state Φ of $$\mathfrak{A}$$ is invariant under the action ofG (in the state space of $$\mathfrak{A}$$ ) iff Φ is αinvariant. Furthermore if the pair { $$\mathfrak{A}$$ ,G} is asymptotically abelian, Φ is ergodic iffμ Φ is ergodic. Transitive ergodic states (corresponding to transitive central measures) are centrally decomposed into primary states whose isotropy groups form a conjugacy class of subgroups. IfG is locally compact and acts continuously on $$\mathfrak{A}$$ , the associated covariant representations of { $$\mathfrak{A}$$ , α} are those induced by such subgroups. Transitive states under timetranslations must be primary if required to be stable. The last section offers a complete classification of the isotropy groups of the primary states occurring in the central decomposition of euclidean transitive ergodic invariant states.
Type of Medium:
Electronic Resource
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