Faddeev-Batalin-Fradkin extended phase space for superparticle quantization

Abstract

Faddeev, Batalin, and Fradkin's (FBF) method of quantization in an extended phase space treats first- and second-class constraints in a symmetrical manner. It is employed here to study a long lasting problem: the covariant quantization of the zero mode of the Green and Schwarz superstring—the superparticle. The essence of this problem lies with the difficulty in covariant separation of first- and second-class constraints in the system. The construction of the FBF extended phase space, its physical content, and its use is explained in detail for several different systems. In the FBF phase space second-class constraints become first class and conventional BRST quantization techniques can be used. The method of FBF is compared to the Stueckelberg-type approach and general conclusions are drawn on restoration of local symmetries in extended phase space. The massive superparticle action is studied and Siegel's local fermionic symmetry in the extended phase space is discussed. The massless limit results in two vector supermultiplets, and the covariant superparticle wave function and propagator are calculated provided certain decoupled fermionic compensators are explicitly retained.