GAUGE PRINCIPLES FOR MULTI-SUPERPARTICLES

We formulate new gauge principles for n supersymmetric particles in a worldline formalism with N supersymmetries. The models provide realiza tions of the more general supersymmetries that are encountered in sect ors of S-theory or Matrix theory, with a superalgebra of the form {Q(a lpha)(A),Q(beta)(B)} = delta(AB)gamma(alpha beta)(mu 1...mu n)(p(mu 1) (1)...p(mu n)(n)). Due to the local gauge and kappa symmetries the n s uperparticle momenta p(i mu) and N supercharges Q(alpha)A are constrai ned by p(i).p(j) = 0 and gamma.p(i)Q(A) = 0. The constraints have solu tions only in a space with n timelike dimensions and SO(d+n-2,n) space time symmetry. The cases SO(9,1), SO(10,2) and SO(10,3), with one, two and three timelike dimensions respectively, are of special interest. In each case, due to the constraints. the classical motion and quantum theory of each superparticle are equivalent to the physics with a sin gle time-like dimension in an effective 10D superspace with SO(9,1) Lo rentz symmetry. (C) 1998 Elsevier Science B.V.