Summary: E0-SEMIGROUPS IN QUANTUM FIELD THEORY
Department of Mathematics
University of California
Berkeley CA 94720, USA
8 July 1994
Abstract. A lecture presented at the von Neumann symposium on Quantization
and Nonlinear Wave Equations held at MIT in June, 1994. We describe the role of
semigroups of endomorphisms of von Neumann algebras in algebraic formulations of
quantum field theory, and present a summary of recent developments in the theory
1991 Mathematics Subject Classification. Primary 46L40; Secondary 81E05.
Key words and phrases. von Neumann algebras, semigroups, automorphism groups, quantum
This research was supported in part by NSF grant DMS92-43893
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2 WILLIAM ARVESON
1. Relation to symmetry groups of algebras of local observables.
In the algebraic formulation of quantum field theory, one works with a C