Quantisation of Klein–Gordon field in $$\\kappa $$κ space-time: deformed oscillators and Unruh effect

Abstract

In this paper we study the quantisation of scalar field theory in $$\\kappa $$-deformed space-time. Using a quantisation scheme that use only field equations, we derive the quantisation rules for deformed scalar theory, starting from the $$\\kappa $$-deformed equations of motion. This scheme allows two choices; (1) a deformed commutation relation between the field and its conjugate which leads to usual oscillator algebra, (2) an undeformed commutation relation between field and its conjugate leading to a deformed oscillator algebra. This deformed oscillator algebra is used to derive modification to Unruh effect in the $$\\kappa $$-space-time.