Confined dynamical systems with Carroll or Galilei symmetries

TL;DR

This paper presents a new method for constructing dynamical systems invariant under Carroll and Galilei symmetries by partitioning space-time and combining invariant actions, enabling the study of confined systems with these symmetries.

Contribution

It introduces a general approach to build invariant dynamical systems under Carroll and Galilei groups using space-time partitioning and separate invariant actions.

Findings

Constructed classes of invariant dynamical systems under Carroll and Galilei groups.

Demonstrated invariance of the total Lagrangian under these symmetries.

Provided a framework for confining systems within these symmetry groups.

Abstract

We introduce a general method to construct classes of dynamical systems invariant under generalizations of the Carroll and of the Galilei groups. The method consists in starting from a space-time in $D+1$ dimensions and partitioning it in two parts, the first Minkowskian and the second Euclidean. Tha action consist of two terms that are separately invariant the Minkwoskian and Euclidean partitioning. One of those contains a system of lagrangian multiplies that confine the system to a subspace. The other term defines the dynamics of the system. The total lagrangian is invariant under the Carroll or the Galilei groups with zero central charge.