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Modular structure of the Weyl algebra

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arxiv 2111.11266 v5 pith:BZKYTJQ3 submitted 2021-11-22 math-ph cs.IThep-thmath.APmath.ITmath.MPmath.OA

classification math-phcs.IThep-thmath.APmath.ITmath.MPmath.OA
keywords algebramodulararakiassociateddimensionsentropygaussianhamiltonian
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We study the modular Hamiltonian associated with a Gaussian state on the Weyl algebra. We obtain necessary/sufficient criteria for the local equivalence of Gaussian states, independently of the classical results by Araki and Yamagami, Van Daele, Holevo. We then present a criterion for a Bogoliubov automorphism to be weakly inner in the GNS representation. We also describe the vacuum modular Hamiltonian associated with a time-zero interval in the scalar, massless, free QFT in two spacetime dimensions, thus complementing the recent results in higher space dimensions. In particular, we have the formula for the local entropy of a one-dimensional massless wave packet and Araki's vacuum relative entropy of a coherent state on a double cone von Neumann algebra.

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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. Excitability in quantum field theory

    hep-th 2026-04 unverdicted novelty 7.0 of 10

    For zero-mean Gaussian states in generalized free field theories, one-way local excitability always implies two-way excitability, generalizing the quasiequivalence theorems of Powers, Stormer, van Daele, Araki, and Yamagami.

  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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