On superpotentials and charge algebras of gauge theories

We propose a new "Hamiltonian inspired" covariant formula to define (withou t harmful ambiguities) the superpotential and the physical charges associat ed to a gauge symmetry. The criterion requires the variation of the Noether current not to contain any derivative terms in partial derivative(mu),delt a(phi). The examples of Yang-Mills (in its first order formulation) and three-dimen sional Chern-Simons theories are revisited and the corresponding charge alg ebras (with their central extensions in the Chern-Simons case) are computed in a straightforward way. We then generalize the previous results to any (2n + 1)-dimensional non-abe lian Chern-Simons theory for a particular choice of boundary conditions. We compute explicitly the superpotential associated to the non-abelian gauge symmetry which is nothing but the Chem-Simons Lagrangian in (2n - 1) dimens ions, The corresponding charge algebra is also computed. However, no associ ated central charge is found for n greater than or equal to 2. Finally, we treat the abelian p-form Chern-Simons theory in a similar way. (C) 1999 Published by Elsevier Science B.V. All rights reserved.