The fermionic massless modular Hamiltonian

TL;DR

This paper derives explicit formulas for the modular Hamiltonian of fermionic massless quantum fields in specific spacetime regions, enabling detailed analysis of their quantum information properties.

Contribution

It provides the first explicit expressions for the modular Hamiltonian of massless fermionic fields in the double cone region, connecting wave solutions to modular dynamics.

Findings

Explicit modular Hamiltonian formulas for Weyl, Dirac, and Majorana fields.

Calculation of relative entropy between vacuum and localized one-particle states.

Enhanced understanding of quantum information measures in fermionic quantum field theories.

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.