Structures of conserved currents and mass spectra for scalar fields: an approach to the generalization of the Goldstone theorem

Abstract

Considering the commutators between a scalar field and a conserved current, we shall clarify the connection between the mass spectrum for a scalar field and the structures of a current. For a special form of currents involving c-number functions, non-invariance of the vacuum under the corresponding transformation entails the existence of a massive mode. It is shown that once a type of currents is specified, the pole structures for [Formula: see text] depend only on c-number parts of Jμ(x). We shall show that the non-vanishing Goldstone commutator does not automatically imply the degeneracy of the vacuum state, and discuss the applicability of the Goldstone theorem.