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Quasi-free isomorphisms of second quantisation algebras and modular theory

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arxiv 2305.07606 v1 pith:SF4VZCLN submitted 2023-05-12 math.OA math-phmath.MP

Roberto Conti , Gerardo Morsella This is my paper · ORCID
classification math.OAmath-phmath.MP
keywords algebrasisomorphismslocalmodularquasi-freesecondabstractapplications
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Using Araki-Yamagami's characterization of quasi-equivalence for quasi-free representations of the CCRs, we provide an abstract criterion for the existence of isomorphisms of second quantization local von Neumann algebras induced by Bogolubov transformations in terms of the respective one particle modular operators. We discuss possible applications to the problem of local normality of vacua of Klein-Gordon fields with different masses.

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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. Uniqueness of null-local modular flow

    hep-th 2026-07 conditional novelty 7.0 of 10

    For the free massless scalar in a Minkowski causal diamond, the vacuum is the unique state or weight in the vacuum sector whose modular flow is local on the null boundary.

  2. 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.

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