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Modular conjugation for multicomponent regions

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arxiv 2209.10711 v2 pith:FVI4PX5N submitted 2022-09-21 hep-th math-phmath.MPquant-ph

Nicolás Abate , David Blanco , Mateo Koifman , Guillem Pérez-Nadal This is my paper · ORCID
classification hep-thmath-phmath.MPquant-ph
keywords modularconjugationmulticomponentanalyticcomputecomputedconsidercontinuation
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We consider a massless Dirac field in $1+1$ 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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Modular evolutions and causality in two-dimensional conformal field theory

    hep-th 2025-01 accept novelty 6.0 of 10

    Modular flows preserve causal spacetime ordering inside causal diamonds, but a bilocal modular Hamiltonian can violate local commutativity at spacelike distances.

  2. Relating the modular Hamiltonian to two-point functions

    math-ph 2025-01 conditional novelty 5.0 of 10

    For free scalar fields in any Gaussian state, the modular Hamiltonian restricted to a region is determined by the equal-time two-point functions X and Π via M=Π^{1/2}B^{-1}arcoth(2B)Π^{1/2}, N=Π^{-1/2}B arcoth(2B)Π^{-...

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