2022/10/18 by Stefano Galanda, Galanda, Stefano
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2210.10746
openalex publication_date 2022/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the relative entropy, in the sense of Araki, for the representation of a self-dual CAR algebra \mathfrakASDC(H,Γ). We notice, for a specific choice of f ∈ H, that the associated element in \mathfrakASDC(H,Γ) is unitary. As a consequence, we explicitly compute the relative entropy between a quasifree state over \mathfrakASDC(H,Γ) and an excitation of it with respect to the abovely mentioned unitary element. The generality of the approach, allows us to consider H as the Hilbert space of solutions of the classical Dirac equation over globally hyperbolic spacetimes, making our result, a computation of relative entropy for a Fermionic Quantum Field Theory. Our result extends those of Longo and Casini et al. for the relative entropy between a quasifree state and a coherent excitation for a free Scalar Quantum Field Theory, to the case of fermions. As a first application, we computed such a relative entropy for a Majorana field on an ultrastatic spacetime.