https://doi.org/10.1140/epjp/s13360-020-00692-2
Regular Article
Phase-space elementary information content of confined Dirac spinors
Departamento de Física, Universidade Federal de São Carlos, PO Box 676, 13565-905, São Carlos, SP, Brazil
Received:
6
April
2020
Accepted:
12
August
2020
Published online:
25
August
2020
Reporting on the Wigner formalism for describing Dirac spinor structures through a covariant phase-space formulation, the quantum information quantifiers for purity and mutual information involving spin–parity (discrete) and position–momentum (continuous) degrees of freedom are consistently obtained. For Dirac spinor Wigner operators decomposed into Poincaré classes of 
spinor couplings, a definitive expression for quantum purity is identified in a twofold way: firstly in terms of phase-space positively defined quantities and secondly in terms of the spin–parity traced-out-associated density matrix in the position coordinate representation, both derived from the original Lorentz-covariant phase-space Wigner representation. Naturally, such a structure supports the computation of relative (linear) entropies, respectively, associated with discrete (spin–parity) and continuous (position–momentum) degrees of freedom. The obtained theoretical tools are used for quantifying (relative) purities, mutual information as well as, by means of the quantum concurrence quantifier, the spin–parity quantum entanglement, for a charged fermion trapped by a uniform magnetic field which, by the way, has the phase-space structure completely described in terms of Laguerre polynomials associated with the quantized Landau levels. Our results can be read as the first step in the systematic computation of the elementary information content of Dirac-like systems exhibiting some kind of confining behavior.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
