Springer Online Journal Archives 1860-2000
Abstract Let us consider a quantum theory of one scalar, real, local, Poincaré covariant fieldA(x) with the restricted spectrum condition (massive one particle states and a unique vacuum). The asymptotic fieldsA in out (x) are assumed to be irreducible. Our conjecture is that under some technical assumptions the “charge” of every real, hermitean, locally conserved, Poincaré covariant quantum (pseudo) vector fieldj μ(x) relatively local toA(x), appearing in this theory-vanishes. This means that in a theory of one scalar, real field with a massive particle one can not expect to get symmetry groups induced by conserved (pseudo) vector currents, only by global, selfadjoint, Poincaré invariant generators. Our arguments can be easily extended to a theory of one complex scalar field, in this case the only symmetry transformation induced by a current can be the gauge transformation. We prove also that under very weak assumptions two fields related to each other by a unitary (or similarity) transformation are equal barring some patological cases.
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