Relating the modular Hamiltonian to two-point functions

2025/01/16 by Markus B. Fröb, Fröb, Markus B. · 1 citation
Mathematics · #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2501.09669

openalex publication_date 2025/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the modular Hamiltonian associated to standard subspaces for a free scalar field in a globally hyperbolic spacetime in an arbitrary Gaussian state. We show how the modular Hamiltonian is related to the two-point function of the theory. For the restriction of the modular Hamiltonian to the subspace, we recover formulas that were obtained previously by Peschel, Casini and Huerta. We also show how the same results can be obtained more directly from the KMS condition, and generalize our results to general CCR algebras.

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