Spontaneously Broken Symmetries and the Question of Massless Particles in a Model Field Theory

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Abstract
An example is given showing that the condition of broken symmetry can be formally satisfied without the presence of interacting masseless particles. The model used is an extension of Zachariasen's model and is a relativistic generalization of the high-density electron gas. The model is defined by a sum of perturbationtheory diagrams and also by an equivalent Lagrangian. In this nodel, when the physical vacuum is not invariant under a certain continuous symmetry of the Lagrangian, massless particles must be present. If, however, a Yukawa interaction of infinite range is present, then these massless mesons decouple from all physical amplitudes.

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