Dynamical rearrangement of symmetries

Abstract

The Goldstone model of a complex scalar field with a biquadratic interaction term in the Lagrangian is studied in the pair approximation. It is found that a zero-mass particle, the Goldstone particle, exists in the symmetry-breaking solution, and that the original symmetry of the theory rearranges itself into the «gauge invariance» of the massless field. The viewpoint adopted is that of “dynamical maps» which allows the theory to be developed clearly and unambiguously, while doing away with the Heisenberg, Schrodinger and interaction representations.