Infinite-Dimensional Algebras as Extensions of Kinematic Algebras

Kinematic algebras can be realised on geometric spaces and constrain the physical models that can live on these spaces. Different types of kinematic algebras exist and we consider the interplay of these algebras for non-relativistic limits of a relativistic system, including both the Galilei and the Carroll limit. We develop a framework that captures systematically the corrections to the strict non-relativistic limit by introducing new infinite-dimensional algebras, with emphasis on the Carroll case. One of our results is to highlight a new type of duality between Galilei and Carroll limits that extends to corrections as well. We realise these algebras in terms of particle models. Other applications include curvature corrections and particles in a background electro-magnetic field.

Automated summary

This paper investigates the kinematic algebras realized on geometric spaces and their constraints on physical models. The authors develop a framework that systematically captures the corrections to the strict non-relativistic limit and introduce new infinite-dimensional algebras. The realization of these algebras using particle models highlights a new type of duality between the Galilei and Carroll limits.