Berry phase effects in the dynamics of Dirac electrons in doubly special relativity framework

Abstract

We consider the Doubly Special Relativity (DSR) generalization of Dirac equation in an external potential in the Magueijo-Smolin base. The particles obey a modified energy-momentum dispersion relation. The semiclassical diagonalization of the Dirac Hamiltonian reveals the intrinsic Berry phase effects in the particle dynamics.

Topics in Noncommutative Geometry Inspired Physics

“…Furthermore the NC quantum theories are qualitatively different with an inherent nonlocality that obviously can not be captured in the canonical set up which, however, provides a very convenient framework to construct the quantum theory. An explicit example is given [177] where we construct the DSR generalization of Dirac fermions in a very simple way as compared to the original derivation [178].…”

“…Hereξ μ is the local translation of the tetrad which must be restricted to the form given in equation (177) in order to preserve the noncommutative algebra (172). The parametersλ ab (x) characterize the local Lorentz transformations atx with ab as the generators of the Lorentz group.…”

Effect of noncommutativity of space-time on Zitterbewegung

“…In this sub-section, we find that how does MS approach of DSR effect on Zitterbewegung. Starting from the deformed dispersion relation in the MS approach of the DSR [35,36] which is given as…”

“…We start with the DSR Dirac equation in the position space in MS base [35,36] and corresponding deformed dispersion relation is given in the above equation. The DSR Dirac equation in MS base is given as [36] 1 + mβ…”

Dirac’s Equation in R-Minkowski Spacetime

“…In the present work, we will focus in the R-Minkowski spacetime on the Dirac equation which is already investigated in the context of the DSR [10,11,12]. Also, we aim to explore more the correspondence, already established in [8], between de Sitter spacetime and the R-Minkowski spacetime.…”