Nambu-Goldstone dynamics and generalized coherent-state functional integrals

TL;DR

This paper introduces a new method using generalized coherent-state functional integrals to analyze Nambu-Goldstone boson dynamics in spontaneously broken theories, exemplified by deriving the ferromagnet's effective Lagrangian and magnon dynamics.

Contribution

It presents a novel approach to Nambu-Goldstone dynamics via coherent-state integrals, applied to ferromagnet low-energy effective theory.

Findings

Derived the Landau-Lifshitz equation from the effective Lagrangian.

Identified Nambu-Goldstone boson as ferromagnetic magnon.

Established a connection between coherent-state integrals and Nambu-Goldstone modes.

Abstract

The present paper gives a new method of attack on the Nambu-Goldstone dynamics in spontaneously broken theories. Since the target space of the Nambu-Goldstone fields is a group coset space, their effective quantum dynamics can be naturally phrased in terms of generalized coherent-state functional integrals. As an explicit example of this line of reasoning we construct a low-energy effective Lagrangian for the Heisenberg ferromagnet in broken phase. The leading field configuration in the WKB approximation leads to the Landau-Lifshitz equation for quantum ferromagnet. The corresponding linearized equations allow to identify the Nambu-Goldstone boson with ferromagnetic magnon.