Endomorphism Semigroups and Lightlike Translations
D. R. Davidson
TL;DR
This paper establishes criteria for when a spatial derivation of a von Neumann algebra generates a one-parameter semigroup of endomorphisms, providing a converse to recent results related to lightlike translations in quantum field theory.
Contribution
It introduces new criteria linking spatial derivations to semigroups of endomorphisms, extending the understanding of lightlike translations in von Neumann algebras.
Findings
Criteria for generating semigroups from spatial derivations
Converse results to Borchers and Wiesbrock on Type III_1 factors
Application to lightlike translations in local observable algebras
Abstract
Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of Wiesbrock on certain one-parameter semigroups of endomorphisms of von Neumann algebras (specifically, Type III_1 factors) that appear as lightlike translations in the theory of algebras of local observables.
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