Nonlinear realizations and the orbit method

TL;DR

This paper explores the relationship between nonlinear realizations and the orbit method for constructing invariant dynamics from symmetry groups, providing insights and examples to compare these approaches.

Contribution

It clarifies the connection between nonlinear realizations and the orbit method, illustrating their relationship with examples.

Findings

The methods are closely related but have distinct features.

Examples demonstrate how each method constructs invariant dynamics.

The paper enhances understanding of symmetry-based modeling techniques.

Abstract

Given a symmetry group one can construct the invariant dynamics using the technique of nonlinear realizations or the orbit method. The relationship between these methods is discussed. Few examples are presented.