VSUSY models with Carroll or Galilei invariance

TL;DR

<3-5 sentences>This work extends a prior method for generating Carroll and Galilei invariant actions to systems with spin described by Grassmann variables in the VSUSY framework. By performing $k$-contractions that respect Poincaré contractions, the authors construct Carroll-type and Galilei-type VSUSY algebras and realize them in both abstract form and configuration space, leading to VSUSY Carroll and VSUSY Galilei particles. Each model possesses a local $\kappa$-symmetry when parameters satisfy $\gamma=-\beta=M$ (Carroll) or $\beta\gamma=M^2$ (Galilei) and yields first-class mass-shell and odd constraints, which quantize to Dirac-type equations in appropriate dimensions. The Appendix shows these actions reproduce standard Carroll and Galilei limits of relativistic spinning particles, validating the contraction approach as a robust route to spinful nonrelativistic and ultra-relativistic systems with VSUSY symmetry.

Abstract

The general method introduced in a previous paperto build up a class of models invariant under generalization of Carroll and Galilei algebra is extended to systems including a set of Grassmann variables describing the spin degree of freedom. The models described here are based on a relativistic supersymmetric algebra with vector and scalar generators (VSUSY) . Therefore, in order to obtain dynamical systems consistent with Carroll or Galilei, we will study the contractions of the anticommuting generators compatible with the Poincaré contractions.