  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.
