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arXiv · 2210.10746

Relative Entropy for Fermionic Quantum Field Theory

Stefano Galanda
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Abstract

We study the relative entropy, in the sense of Araki, for the representation of a self-dual CAR algebra $\mathfrak{A}_{SDC}(\mathcal{H},\Gamma)$. We notice, for a specific choice of $f \in \mathcal{H}$, that the associated element in $\mathfrak{A}_{SDC}(\mathcal{H},\Gamma)$ is unitary. As a consequence, we explicitly compute the relative entropy between a quasifree state over $\mathfrak{A}_{SDC}(\mathcal{H},\Gamma)$ and an excitation of it with respect to the abovely mentioned unitary element. The generality of the approach, allows us to consider $\mathcal{H}$ 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.

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Stefano Galanda. 2022-10-18. Relative Entropy for Fermionic Quantum Field Theory. https://arxiv.org/abs/2210.10746

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