On the Symmetric Space Sigma-Model Kinematics

TL;DR

This paper explores the parametrization of symmetric spaces using solvable Lie algebras and compares two formulations of the symmetric space sigma model, establishing their equivalence through normalization and field transformations.

Contribution

It provides a detailed analysis of solvable Lie algebra parametrizations and demonstrates the equivalence of two formulations of the sigma model.

Findings

Two equivalent formulations of the symmetric space sigma model are identified.

Normalization conditions and field transformations establish the correspondence between formulations.

The solvable Lie algebra gauge offers a unified framework for symmetric space parametrization.

Abstract

The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.