Appropriate linearizations of interacting theories with spontaneous symmetry breaking

Abstract

Spontaneous breakdown of a symmetry group in a dynamical theory is connected with a rearrangement of group properties between quantized and classical degrees of freedom enforced by the classical asymmetry properties of the ground state. By disentangling the classical and quantized parts in the original basic field operators, designed for describing the short-distance behaviour, and by rearranging them in various ways, new dressed field operators with different symmetry properties, adapted to the description in the asymptotic region, can be constructed which, in general, admit more appropriate linearizations of the theory and hence offer better starting points for a perturbative treatment of the interaction. There are essentially two different dressing mechanisms of the basic field by which fields with particle interpretation are generated: an asymmetric dressing which relies strongly on the asymmetry of the ground state and a symmetric dressing which is only triggered by it. The formalism is exemplified for the nonlinear chiral model of Nambu and Jona-Lasinio. The main purpose of the paper, however, does not aim at improving the approximations in this model, but is thought of as a preparation for a similar treatment of more realistic theories with a spontaneous breakdown of a non-Abelian symmetry group and of the dilatation group in which these considerations may offer natural explanations for the occurrence of approximate higher symmetries and for the mysterious coexistence of two types of particles, the leptons and gauge particles on the one hand and the hadrons on the other hand.