Modular conjugation for multicomponent regions
Nicol\'as Abate, David Blanco, Mateo Koifman, Guillem P\'erez-Nadal
TL;DR
This paper computes the modular conjugation for a massless Dirac field in 1+1 dimensions over multicomponent regions, using analytic continuation from the modular flow, and discusses Haag duality in this context.
Contribution
It provides a novel calculation of the modular conjugation for multicomponent regions in a massless Dirac field, extending previous modular flow results.
Findings
Derived explicit form of modular conjugation for multicomponent regions.
Analyzed the implications for Haag duality in the model.
Extended understanding of modular structures in quantum field theory.
Abstract
We consider a massless Dirac field in dimensions, and compute the Tomita-Takesaki modular conjugation corresponding to the vacuum state and a generic multicomponent spacetime region. We do it by analytic continuation from the modular flow, which was computed recently. We use our result to discuss the validity of Haag duality in this model.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Advanced Algebra and Geometry · Quantum Chromodynamics and Particle Interactions