Systems with Carrollian symmetry

Abstract

The Carrollian limit can be obtained by starting from a relativistic system and collapsing the lightcone. This can be contrasted with the Galilean limit, which can be seen as opening up the lightcone. The Galilean limit results in a system with Galilean symmetry. Similarly, the Carrollian limit results in a system with Carrollian symmetry. In this thesis we clarify how to arrive at Carrollian systems. In order to do this we contrast two different approaches. The first approach consists of an explicit coordinate transformation. This is akin to closing up the light cone in a relativistic system. This leads to interesting interpretations such as the Carrollian particles becoming static or tachyonic. By using the first approach we arrive at a set of particles that could potentially describe physics in a hyper-relativistic regime, such as near the event horizon of a black hole. Another approach involves an embedding into Bargmann space. By embedding a Carrollian structure into a manifold exhibiting Bargmann symmetry we find a more general class of Carrollian systems, not all of which are given by a taking the limit on a relativistic system.