Geometry of Classical Nambu-Goldstone Fields

TL;DR

This paper introduces a coordinate-free, symmetry-based framework for describing Nambu-Goldstone fields as sections on associated bundles, enabling classification without relying on effective Lagrangians.

Contribution

It presents a novel geometric formulation that directly derives the number and types of Nambu-Goldstone fields from symmetry considerations alone.

Findings

Provides a coordinate-free, symmetry-based description of Nambu-Goldstone fields.

Shows Lorentz-symmetry breaking induces a symplectic structure in field space.

Enables classification of Nambu-Goldstone fields without effective Lagrangian reference.

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.