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

## TL;DR

This paper explores the quantisation of scalar fields in $$-deformed space-time, deriving new oscillator algebra relations and examining their impact on the Unruh effect.

## Contribution

It introduces a novel quantisation scheme for $$-deformed scalar fields, allowing for different oscillator algebra formulations and analyzing their physical implications.

## Key findings

- Derived quantisation rules for $$-deformed scalar fields.
- Established a connection between deformed oscillator algebra and the Unruh effect.
- Proposed two quantisation schemes with distinct algebraic structures.

## 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; (i)a deformed commutation relation between the field and its conjugate which leads to usual oscillator algebra, (ii) 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.