The fermionic massless modular Hamiltonian
Mathematical Physics
2025-03-18 v2 Information Theory
math.IT
math.MP
Operator Algebras
Abstract
We provide an explicit expression for the modular hamiltonian of the von Neumann algebras associated to the unit double cone for the (fermionic) quantum field theories of the 2-component Weyl (helicity 1/2) field, and of the 4-component massless Dirac and Majorana fields. To this end, we represent the one particle spaces of these theories in terms of solutions of the corresponding wave equations, and obtain the action of the modular group on them. As an application, we compute the relative entropy between the vacuum of the massless Majorana field and one particle states associated to waves with Cauchy data localized in the spatial unit ball.
Cite
@article{arxiv.2405.07888,
title = {The fermionic massless modular Hamiltonian},
author = {Francesca La Piana and Gerardo Morsella},
journal= {arXiv preprint arXiv:2405.07888},
year = {2025}
}
Comments
24 pages, one figure. One figure and several explanations added. Version accepted for publication