LORENTZ-HARMONIC (SUPER)FIELDS AND (SUPER)PARTICLES

We apply the recently developed concept of a compact Lorentz-harmonic space, which is isomorphic to the sphere S(D-2), to the problem of covariant quantization of the superparticle in D = 3, 4, 6, 10. We study the structure of the representation of the Lorentz group realized on harmonic functions on S(D-2). The crucial difference between compact and non-compact harmonic analysis is explained. The massless harmonic fields depend on one space-time coordinate x++ only, and on D - 2 harmonic coordinates. It is shown how ordinary massless fields can be obtained from the harmonic ones by means of covariant integration on S(D-2). We construct a Lorentz-harmonic superspace, which involves only one quarter of the usual number of Grassmann coordinates. It closely resembles the light-cone superspace, however it is Lorentz covariant. This framework is used to formulate a superparticle action, in which all the constraints are first class, Lorentz-covariant and allow a straightforward canonical quantization.