Supersymmetric properties and stability of the Dirac sea

Three-dimensional Dirac oscillator in a thermal bath

“…The reason for this is twofold. First, the Hamiltonian for the Dirac oscillator admits an exact Foldy-Wouthuysen transformation (FWT), such that the positive-and negative-energy solutions never mix, leaving the Dirac sea stable [19,20]. Consequently, we can assume that only particles with positive energy are available in order to set up a thermodynamic ensemble.…”

Superconformal Quantum Mechanics via Wigner–heisenberg Algebra

“…One motivation for this work is the future applications in the problems related to black holes [2,7] and the construction of a supersymmetric quantum mechanics with conformal symmetry for the n-particles in the Wigner-Heisenberg picture. Let us point out that one can consider the same analysis implemented in this work for the Dirac oscillator, getting a generalization of the works [21,26,27].…”

“…Another application for these models is in the study of the radial motion of test particle near the horizon of extremal Reissner-Nordström black holes [6,7]. Also, another interesting application of the superconformal symmetry is the treatment of the Dirac oscillator [21,22].…”

“…We remark that since h,h and H 0 commute with each other, they form a set of mutually commuting operators. The superhamiltonian h andh are extensions of the ones in references [21,22] for the superconformal Dirac oscillator.…”

The Wigner-Heisenberg Algebra in Quantum Mechanics

“…Another application for these models is in the study of the radial motion of test particle near the horizon of extremal Reissner-Nordström black holes [35,37]. Also, another interesting application of the superconformal symmetry is the treatment of the Dirac oscillator, in the context of the superconformal quantum mechanics [39][40][41][42]46].…”