Induced representations of C∗-algebras

Starting from an algebra of fields
 
$$\mathfrak{F}$$

 and a compact gauge group of the first kind ℊ, the observable algebra
 
$$\mathfrak{A}$$

 is defined as the gauge invariant part of
 
$$\mathfrak{F}$$

 . A gauge group of the first kind is shown to be automatically compact if the scattering states are complete and the mass and spin multiplets have finite multiplicity. Under reasonable assumptions about the structure of
 
$$\mathfrak{F}$$

 it is shown that the inequivalent irreducible representations of
 
$$\mathfrak{A}$$

 (“sectors”) which occur are in one-to-one correspondence with the inequivalent irreducible representations of ℊ and that all of them are “strongly locally equivalent”. An irreducible representation of
 
$$\mathfrak{A}$$

 satisfies the duality property only if the sector corresponds to a 1-dimensional representation of ℊ. If ℊ is Abelian the sectors are connected to each other by localized automorphisms.

/pdf/fields-observables-and-gauge-transformations-i-2phm6695oj.pdf

Fields, observables and gauge transformations I

Standard and split inclusions of von Neumann algebras

We study the class of stationary states and the domain of attraction of each of them, for a dynamical semigroup possessing a faithful normal stationary state. We give applications to the approach to stationarity of an open quantum system, and to models of the quantum measurement process.

/pdf/stationary-states-of-quantum-dynamical-semigroups-5cy5uhdurj.pdf

Stationary States of Quantum Dynamical Semigroups

We consider theC*-algebras which contain the Weyl operators when the symplectic form which defines the C.C.R. is possibly degenerate. We prove that the C.C.R. are all obtained as a quotient of a universalC*-algebra by some of its ideals, and we characterize all these ideals.

/pdf/the-smallest-c-algebra-for-canonical-commutations-relations-1uggo5jff8.pdf

E Størmer

Papers

Invariant states and asymptotic abelianness