Geometry of classical Nambu–Goldstone fields

Abstract

A coordinate-free formulation of first order effective field theory, in which Nambu–Goldstone fields are described as sections on associated bundle, is presented. This construction, which is based only on symmetry considerations, allows for a direct derivation of number and types of Nambu–Goldstone fields in a classical field theory without any reference to effective Lagrangian. A central role in classification is shown to be played by Lorentz-symmetry breaking order parameter which induces symplectic structure in the field space of the theory.