The Fermionic Massless Modular Hamiltonian
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.
Authors
- Gerardo Morsella (ORCID: https://orcid.org/0000-0003-2370-6308)
- Francesca La Piana
Institutions
- University of Rome Tor Vergata (IT)
- University of Oslo (NO)
Publication Details
- Journal
- Communications in Mathematical Physics
- Published
- 2025-03-05
- DOI
- https://doi.org/10.1007/s00220-025-05253-1
- Citations
- 1
- Primary Topic
- Spectral Theory in Mathematical Physics
- Type
- article
- Field-Weighted Citation Impact
- 3.69
Funders
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Trond Mohn stiftelse
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Norges Forskningsråd
- Università degli Studi di Roma Tor Vergata
- Ministero dell'Università e della Ricerca
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- European Research Council