Quantization of κ-deformed Dirac equation

Abstract

In this paper, we study the quantization of Dirac field theory in the κ-deformed space-Time. We adopt a quantization method that uses only equations of motion for quantizing the field. Starting from κ-deformed Dirac equation, valid up to first order in the deformation parameter a, we derive deformed unequal time anticommutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anticommutation relations between κ-deformed spinor and its adjoint, we also derive a deformed oscillator algebra. We show that deformed number operator is the conserved charge corresponding to global phase transformation symmetry. We construct the κ-deformed conserved currents, valid up to first order in a, corresponding to parity and time-reversal symmetries of κ-deformed Dirac equation also. We show that these conserved currents and charges have a mass-dependent correction, valid up to first order in a. This novel feature is expected to have experimental significance in particle physics. We also show that it is not possible to construct a conserved current associated with charge conjugation, showing that the Dirac particle and its antiparticle satisfy different equations in κ space-Time.