Conformal invariance in a Dirac oscillator

Abstract

The conformal invariance properties of a Dirac oscillator are established. A set of operators is constructed whose algebra shows that it can be considered as a conformal system. The operators are then used to solve the problem using algebraic techniques. The superconformal generalization of the algebra is also worked out, and some consequences of these invariances for the properties of the model are mentioned.

The Statistical Properties of theq-Deformed Dirac Oscillator in One and Two Dimensions

“…The interest in the problem was revived by Moshinsky and Szczepaniak [18], who gave it the name of DO because, in the nonrelativistic limit, it becomes a harmonic oscillator with a very strong spin-orbit coupling term. Physically, it can be shown that the DO interaction is a physical system, which can be interpreted as the interaction of the anomalous magnetic moment with a linear electric field [19,20]. The electromagnetic potential associated with the DO has been found by Benitez et al [21].…”

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].…”

Superconformal Quantum Mechanics via Wigner–heisenberg Algebra

“…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.…”