content_image/306704.jpg content_image/306705.jpg content_image/306706.jpg content_image/306707.jpg
## Appendix B 

## Field Theory Derivation of Elastic Scattering Cross-section between φ and a Thermal Bath 

We assume the thermal bath to only consist of one scalar field, which we call χ . We define the following 4-momenta: p$_{1}$ for a φ particle before the collision, p$_{2}$ for a χ particle before the collision, p$_{3}$ for a φ particle after the collision and p$_{4}$ for a χ particle after the collision. Working within the centre-of-mass frame, the 4-momenta are: 

<img src='content_image/306704.jpg'>

<img src='content_image/306705.jpg'>

<img src='content_image/306706.jpg'>

<img src='content_image/306707.jpg'>

