2002/04/19 by M. A. Vasiliev
Physics and Astronomy · #hep-th
published as Russ.Phys.J. 45 (2002) 670-681; Izv.Vuz.Fiz. 2002N7 (2002) 23-34 · Latex, 16 pages; no figures. Contribution to Quantum Field Theory, Gravity and Strings. Special issue of the Russian Physcs Journal dedicated to century of Tomsk State Pedagogical University
arxiv created 2002/04/19 · arxiv updated 2009/11/30
Infinite set of higher spin conserved charges is found for the sp(2M) symmetric dynamical systems in \f12 M (M+1)-dimensional generalized spacetime \MM. Since the dynamics in \MM is equivalent to the conformal dynamics of infinite towers of fields in d-dimensional Minkowski spacetime with d=3,4,6,10,... for M=2,4,8,16, ..., respectively, the constructed currents in \MM generate infinite towers of (mostly new) higher spin conformal currents in Minkowski spacetime. The charges have a form of integrals of M-forms which are bilinear in the field variables and are closed as a consequence of the field equations. Conservation implies independence of a value of charge of a local variation of a M-dimensional integration surface Σ⊂ \MM analogous to Cauchy surface in the usual spacetime. The scalar conserved charge provides an invariant bilinear form on the space of solutions of the field equations that gives rise to a positive definite norm on the space of quantum states.