Alternative Approaches to the Casalbuoni–Brink–Schwarz Superparticle

✍ Scribed by Morten Nielsen; N.K. Nielsen

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 223 KB
• Volume: 285
• Category: Article
• ISSN: 0003-4916
• DOI: 10.1006/aphy.2000.6083

✦ Synopsis

Wigner's method of induced representations is applied to the N=1 super-Poincare group, and by using a state corresponding to the basic vector of the little group as a Clifford vacuum we show that the spin operator of a supersymmetric point particle obeys Wigner's constraints. As dynamical variables for the particle we use canonical coordinates on the symmetry group manifold. The physical phase space is then constructed using a vielbein formalism. We find that the Casalbuoni Brink Schwarz superparticle appears as a special case of our general construction. Finally, the theory is reformulated as a gauge theory where the gauge freedom corresponds to the choice of spin constraints or, equivalently, the free choice of relativistic center of mass. In a special case the gauge symmetry reduces to the well known }-symmetry.