Galilean Exotic Planar Supersymmetries and Nonrelativistic Supersymmetric Wave Equations
J. Lukierski (Wroclaw Univ. Poland), I. Prochnicka (Wroclaw Univ., Poland), P.C. Stichel (Bielefeld, Germany), W.J. Zakrzewski (University of, Durham, UK)
TL;DR
This paper explores the structure of extended Galilean supersymmetries in (2+1) dimensions derived from Poincaré superalgebras, confirming the role of exotic central charges and formulating a superfield equation for nonrelativistic particles.
Contribution
It introduces a comprehensive class of N-extended Galilean superalgebras with exotic central charges and develops a superfield equation for nonrelativistic particles.
Findings
Confirmed consistency of exotic central charge with supersymmetry
Derived N=2 Galilean superfield equation for free particles
Extended supersymmetry algebra classification in (2+1) dimensions
Abstract
We describe the general class of -extended Galilean supersymmetries obtained, respectively, from the -extended D=3 Poincar\'{e} superalgebras with maximal sets of central charges. We confirm the consistency of supersymmetry with the presence of the `exotic' second central charge . We show further how to introduce a N=2 Galilean superfield equation describing nonrelativistic spin 0 and spin 1/2 free particles.
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