Generalized canonical approach to gyrokinetic theory

TL;DR

This paper introduces a novel formulation for gyrokinetic theory that constructs canonical variables through a new definition of canonical transformation, clarifying longstanding ambiguities in the field.

Contribution

It proposes an innovative method to define canonical variables in gyrokinetic theory, reducing ambiguities caused by field-related canonical coordinates.

Findings

New canonical transformation framework for gyrokinetics

Clarification of canonical variable construction

Potential to resolve existing controversies in the field

Abstract

We face the well-known gyrokinetic problem, which arises in the description of the dynamics of a charged particle subject to fast gyration for the presence of a strong electromagnetic field. The customary approach to gyrokinetic theory, using canonical variables or identifying them ``a posteriori'' by means of Darboux theorem, leads to potential complications and ambiguities due to the fact that canonical coordinates are field-related. Here we propose an innovative formulation to construct gyrokinetic canonical variables based on the introduction of a new definition of canonical transformation. The new approach permits to shed light on this often controversial issue.