Phase-space elementary information content of confined Dirac spinors
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Phase-space elementary information content of confined Dirac spinors Alex E Bernardinia Departamento de Física, Universidade Federal de São Carlos, PO Box 676, São Carlos, SP 13565-905, Brazil Received: 6 April 2020 / Accepted: 12 August 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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 SU(2) ⊗ SU(2) 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.
1 Introduction Enlarging the access to elementary information features of physical systems without affecting the predictive power of quantum mechanics, the Wigner phase-space representation [1–4] of quantum mechanics has currently shed some light on the investigation of the frontiers between classical and quantum descriptions of nature [5–10]. Besides its ferramental pragmatic utility demanded by optical quantum mechanics [11], in the theoretical front, the Wigner quantum mechanics has also worked as a robust support for the non-commutative quantum mechanics [12–21], for the description of the flux of quantum information in the phase space [22– 25] and, more generically, for probing quantumness and classicality for a relevant set of anharmonic quantum systems [24,26,27] as well as for quantitative modeling beyond the quantum physical framework [28].
a e-mail: [email protected] (corresponding author)
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Recently, the framework has also been investigated in the context of lattice-regularized quantum field theories and of lattice models of solid-state physics [29–31], from which a subtle connection with Dirac qua
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