Abstract
Generalization of the Goldstone theorem and of the Coleman theorems are formulated and proven within the framework of the Wightman field theory. The generalization of the Goldstone theorem is to a class of currents in which implicit and explicit co-ordinate dependence are mixed. We get that vacuum noninvariance entails the existence of certain masses in the energy-momentum spectrum which are not necessarily zero. The generalizations of the Coleman theorems are to local tensor fields and to several classes of fields in which implicit and explicit co-ordinate dependence are mixed. Several examples are examined in light of the new theorems.
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