Relative Entropy of Fermion Excitation States on the CAR Algebra
- URL: http://arxiv.org/abs/2305.02788v1
- Date: Thu, 4 May 2023 12:42:24 GMT
- Title: Relative Entropy of Fermion Excitation States on the CAR Algebra
- Authors: Stefano Galanda, Albert Much, Rainer Verch
- Abstract summary: The relative entropy of certain states on the algebra of canonical anticommutation relations is studied.
The CAR algebra is used to describe fermionic degrees of freedom in quantum mechanics and quantum field theory.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: The relative entropy of certain states on the algebra of canonical
anticommutation relations (CAR) is studied in the present work. The CAR algebra
is used to describe fermionic degrees of freedom in quantum mechanics and
quantum field theory. The states for which the relative entropy is investigated
are multi-excitation states (similar to multi-particle states) with respect to
KMS states defined with respect to a time-evolution induced by a unitary
dynamical group on the one-particle Hilbert space of the CAR algebra. If the
KMS state is quasifree, the relative entropy of multi-excitation states can be
explicitly calculated in terms of 2-point functions, which are defined entirely
by the one-particle Hilbert space defining the CAR algebra and the Hamilton
operator of the dynamical group on the one-particle Hilbert space. This applies
also in the case that the one-particle Hilbert space Hamilton operator has a
continuous spectrum so that the relative entropy of multi-excitation states
cannot be defined in terms of von Neumann entropies. The results obtained here
for the relative entropy of multi-excitation states on the CAR algebra can be
viewed as counterparts of results for the relative entropy of coherent states
on the algebra of canonical commutation relations (CCR) which have appeared
recently. It turns out to be useful to employ the setting of a self-dual CAR
algebra introduced by Araki.
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