An Algebraic Characterization of Vacuum States in Minkowski Space. III. Reflection Maps

Abstract

Employing the algebraic framework of local quantum physics, vacuum states in Minkowski space are distinguished by a property of geometric modular action. This property allows one to construct from any locally generated net of observables and corresponding state a continuous unitary representation of the proper Poincare group which acts covariantly on the net and leaves the state invariant. The present results and methods substantially improve upon previous work. In particular, the continuity properties of the representation are shown to be a consequence of the net structure, and surmised cohomological problems in the construction of the representation are resolved by demonstrating that, for the Poincare group, continuous reflection maps are restrictions of continuous homomorphisms.

arXiv comment20 pages; change of title, reference added; version as to appear in Commun. Math. Phys

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• Spin, Statistics, and Reflections, I. Rotation Invariance
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• Inequivalent Vacuum States in Algebraic Quantum Theory
• Axiomatic quantum field theory. Jet formalism