# Quantized Scalar Fields in Curved Spacetime Background of Thick Brane

## TL;DR

This paper quantizes a scalar field in a curved brane background, analyzes particle creation due to a classical source, and explores how extra dimensions influence particle modes and densities.

## Contribution

It introduces a method to quantize scalar fields in a thick brane background and studies particle production, highlighting effects of extra dimensions on excited modes.

## Key findings

- Particle numbers depend on the detection of ground or excited states.
- Extra dimensions significantly affect the particle number density.
- The method provides insights into quantum effects in braneworld scenarios.

## Abstract

In this paper, we adopt the method of quantum fields in curved spacetime to quantize a free scalar matter field in the braneworld background whose warped factor is of the form that could generate P\"{o}schl-Teller potential. Then we consider the interaction between the scalar field $\phi(x)$ and a classical scalar source $\rho(x)$ with the form $\mathcal{H}_I=\sqrt{-g}\tilde{g}\rho(x)\phi(x)$. The corresponding S-matrix is given and the number of particles generated by the source is obtained. Furthermore, we get the {particle numbers} in the cases that only ground state mode of the field could be detected and both the ground and first exited states could be detected, respectively. Finally, by the particle number density we define, we show how the extra dimension makes a difference specifically by the excited modes.