Quantisation of $κ$-deformed Dirac equation

Abstract: In this paper, we study the quantisation of Dirac field theory in the $\kappa$-deformed space-time. We adopt a quantisation method that uses only equations of motion for quantising the field. Starting from $\kappa$-deformed Dirac equation, valid up to first order in the deformation parameter $a$, we derive deformed unequal time anti-commutation relation between deformed field and its adjoint, leading to undeformed oscillator algebra. Exploiting the freedom of imposing a deformed unequal time anti-commutation relations between $\kappa$-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 $\kappa$-deformed conserved currents, valid up to first order in $a$, corresponding to parity and time-reversal symmetries of $\kappa$-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 anti-particle satisfy different equations in $\kappa$-space-time.