Higher-rank fields and currents

Abstract

Sp(2M) invariant field equations in the space ℳM with symmetric matrix coordinates are classified. Analogous results are obtained for Minkowski-like subspaces of ℳM which include usual 4d Minkowski space as a particular case. The constructed equations are associated with the tensor products of the Fock (singleton) representation of Sp(2M) of any rank r. The infinite set of higher-spin conserved currents multilinear in rank-one fields in ℳM is found. The associated conserved charges are supported by rM−r(r−1)2-dimensional differential forms in ℳM , that are closed by virtue of the rank-2r field equations. The cohomology groups Hp(σ−r) with all p and r, which determine the form of appropriate gauge fields and their field equations, are found both for ℳM and for its Minkowski-like subspace.