Generalized Killing Equations and Symmetries of Spinning Space

摘要

The authors derive a set of general conditions for the isometries of d-dimensional spinning space. These equations constitute a Grassmann-valued extension of the Killing equations for ordinary space. They are realized as invariances of spinning-particle actions. Some general solutions for the extended Killing equations in arbitrary curved space are presented. Thus the spinning particle in d dimensions can be shown to possess new types of (super-) symmetries, which transform the commuting and anti-commuting co-ordinates ((x sup mu), (Psi sup a)) not only linearly, but also non-linearly. The algebra of these non-linear transformations is presented. A complete solution of the generalized Killing equations is given for flat spinning space and an infinite set of conserved charges is constructed.