# Low energy dynamics of spinor condensates

## TL;DR

This paper derives a low energy Lagrangian for the spin dynamics in spinor Bose condensates with zero average magnetization, extending previous models to all phases except ferromagnetic ones.

## Contribution

It provides a sigma model-based Lagrangian for spin dynamics applicable to multiple phases of spinor condensates, excluding ferromagnetic phases.

## Key findings

- Derived the low energy Lagrangian for spinor condensates.
- Extended the sigma model description to various phases.
- Clarified the dynamics in non-ferromagnetic phases.

## Abstract

We present a derivation of the low energy Lagrangian governing the dynamics of the spin degrees of freedom in a spinor Bose condensate, for any phase in which the average magnetization vanishes. This includes all phases found within mean-field treatments except for the ferromagnet, for which the low energy dynamics has been discussed previously. The Lagrangian takes the form of a sigma model for the rotation matrix describing the local orientation of the spin state of the gas.