Current Algebras at Infinite Momentum

Abstract

We examine the mathematical properties of the "infinite-momentum limit" of current-density operators. Free-field currents are examined for heuristic purposes. For physical particles we consider the restrictions of the current-density operators to the one-particle subspace. The existence of an operator limit is demonstrated for scalars, vectors, and antisymmetric tensors. The limit vanishes for scalars and, except in special cases, diverges for higher tensors. The kernels of the limit operators are obtained explicitly as functions of the same invariant form factors that determine the kernels of the original current densities. Commutation relations for the integrated currents are dynamical hypotheses. "Local" commutation relations for the densities at infinite momentum are incompatible with the assumption that the spins are bounded in the one-particle subspace.