Nonrelativistic anti-Snyder model and some applications

Abstract

In this paper, we examine the (2[Formula: see text]+[Formula: see text]1)-dimensional Dirac equation in a homogeneous magnetic field under the nonrelativistic anti-Snyder model which is relevant to doubly/deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigensolutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states [Formula: see text] due to the orthogonality of the polynomials and the maximum energy is truncated at [Formula: see text]. Similar to the minimal length case, the degeneracy of the Dirac–Landau levels in anti-Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit [Formula: see text]. By taking [Formula: see text], we explore the motion of effective massless charged fermions in graphene-like material and obtained a maximum bound of deformed parameter [Formula: see text]. Furthermore, we consider the modified energy dispersion relations and its application in describing the behavior of neutrinos oscillation under modified commutation relations.