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

TL;DR

This paper uses algebraic quantum physics to characterize Minkowski space vacuum states via geometric modular action, enabling the construction of Poincare group representations with improved continuity and reflection properties.

Contribution

It provides a novel algebraic approach to construct covariant Poincare group representations from local nets, resolving previous cohomological issues and establishing continuity from net structure.

Findings

Constructed continuous unitary representations of the Poincare group from local quantum nets.

Proved that continuity properties follow from the net structure.

Demonstrated that reflection maps are restrictions of continuous homomorphisms.

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.