Relating the modular Hamiltonian to two-point functions
Mathematical Physics
2025-02-25 v2 math.MP
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.
Cite
@article{arxiv.2501.09669,
title = {Relating the modular Hamiltonian to two-point functions},
author = {Markus B. Fröb},
journal= {arXiv preprint arXiv:2501.09669},
year = {2025}
}
Comments
20 pages, added details and generalization to general CCR algebras