Vector SUSY models with Carroll or Galilei invariance

Andrea Barducci,Joaquim Gomis,Roberto Casalbuoni

doi:10.1103/physrevd.99.045016

Andrea Barducci, Joaquim Gomis + Show 1 more

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https://doi.org/10.1103/physrevd.99.045016

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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 Poincar\'e contractions.

Highlights

In a previous paper [1] we have introduced a general strategy to build up a class of models invariant under generalizations of Carroll and Galilei algebra with zero central charge [2,3,4,5,6,7,8,9,10] A bonus of this approach is that it allows a description in configuration space, whereas most of the models invariant under Carroll or Galilei group present in the literature are described by an action in phase space
The aim of this work is to apply this method to systems including a set of Grassmann variables describing the spin degrees of freedom, exhibiting a Carroll or a Galilei symmetry
The system we have in mind is one with a SUSY symmetry described by vectorlike and scalar anticommuting generators (VSUSY)

Summary

INTRODUCTION

In a previous paper [1] we have introduced a general strategy to build up a class of models invariant under generalizations of Carroll and Galilei algebra with zero central charge [2,3,4,5,6,7,8,9,10] A bonus of this approach is that it allows a description in configuration space, whereas most of the models invariant under Carroll or Galilei group present in the literature are described by an action in phase space. The system we have in mind is one with a SUSY symmetry described by vectorlike and scalar anticommuting generators (VSUSY) This algebra, which is a relativistic one, was introduced in [11], in order to get a “pseudoclassical” description of the Dirac equation. The models we would like to construct here should exhibit Carroll or Galilei supersymmetry counterpart To this end, we would need to construct specific contractions of VSUSY algebra. A Carroll or Galilei invariant model can be obtained by introducing a Minkowski invariant action, or Euclidean invariant action respectively, in one of the partitions of the space-time (the Minkowskian for Carroll or the euclidean for Galilei) and, in the complementary partition, a system of lagrange multipliers transforming in an appropriate way under the. In the Appendix we show how the actions, for the VSUSY Carroll and Galilei particle, can be derived by performing the standard Carroll and nonrelativistic limiting procedures in the Poincareinvariant phase space action

POINCARÉ CONTRACTIONS

VSUSY CONTRACTIONS

THE VSUSY CARROLL PARTICLE

Quantization

THE VSUSY GALILEI PARTICLE

CONCLUSIONS