Endomorphism semigroups and lightlike translations
Copyright policy )Endomorphism semigroups and lightlike translations
Borchers and Wiesbrock have demonstrated certain results concerning the one-parameter semigroups of endomorphisms of von Neumann algebras that appear as lightlike translations in the theory of algebras of local observables. These results are abstracted and analyzed as essentially operator-theoretic. Criteria are then demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms. All this is combined to establish a von Neumann-algebraic converse to the Borchers-Wiesbrock results. This analysis is then applied to questions of isotony and covariance for local algebras.
16 pages, Latex; minor corrections
- Sapienza University of Rome Italy
- Roma Tre University Italy
High Energy Physics - Theory, modular automorphisms, Mathematics - Operator Algebras, Borcher's theorem, FOS: Physical sciences, Poincaré covariance, one-parameter semigroups of endomorphisms of von Neumann algebras, lightlike translations, algebras of local observables, Axiomatic quantum field theory; operator algebras, Functional Analysis (math.FA), velocity transformations, Mathematics - Functional Analysis, Applications of functional analysis in quantum physics, High Energy Physics - Theory (hep-th), Applications of selfadjoint operator algebras to physics, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Noncommutative dynamical systems, Operator Algebras (math.OA), modular covariance
High Energy Physics - Theory, modular automorphisms, Mathematics - Operator Algebras, Borcher's theorem, FOS: Physical sciences, Poincaré covariance, one-parameter semigroups of endomorphisms of von Neumann algebras, lightlike translations, algebras of local observables, Axiomatic quantum field theory; operator algebras, Functional Analysis (math.FA), velocity transformations, Mathematics - Functional Analysis, Applications of functional analysis in quantum physics, High Energy Physics - Theory (hep-th), Applications of selfadjoint operator algebras to physics, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Noncommutative dynamical systems, Operator Algebras (math.OA), modular covariance
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