Carrollian Physics and its Thermodynamics description

Abstract

Carroll symmetry emerges as a consequence of the limit where the speed of light tends to zero, starting from Poincaré symmetry. Further, it is expected that the Carrollian thermodynamics description in the strict Carroll limit in different frameworks gives a cosmological equation of state $\mathcal{E}+\mathcal{P}=0$. To establish a rigorous thermodynamic setup, both for the individual particles and massless scalar quantum field theories we employ an imaginary chemical potential conjugate to momentum. Then we focus on the diagonality condition of the stress energy tensor in the Carroll regime and the leading term in $\left(\frac{c}{v}\right)$- expansion. The conjecture linking Carroll conformal field theories with flat space holography regarding the $BMS_3$ group, potentially extending to de Sitter spacetime is gaining traction. This study holds seeds for the relevance of Carroll physics to dark energy and inflation. To make this master thesis self-consistent there is a brief review including Carroll particles and Carroll quantum field theories that contains some new material. The electric and magnetic sectors are presented and in thermodynamics, they appear to exhibit uniform behavior in the massless case.