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: 121 p$_{1}$ = ( E$_{1}$, p ) (B.1) p$_{2}$ = ( p, − p ) (B.2) p$_{3}$ = ( E$_{3}$, $_{p}$′$_{)}$ (B.3) p$_{4}$ = ( p ′ , − $_{p}$′$_{)}$ (B.4)