ABSTRACT
This chapter examines the construction from its infinitesimal elements of a continuous group of canonical transformations, where a transformation must be completely specified by the values of the parameters and thus is independent of the integration path. The quadratic connections among the g coefficients, comprised in the commutation relations, are identical with the conditions of integrability for the differential equations, which verifies the consistency of the operator presentation. Groups of the latter type are necessarily semi-simple, by which is meant that they possess no Abelian invariant subgroups. The significance of these terms can be given within the framework of infinitesimal transformations. The ability to integrate over the group manifold is particularly valuable when the group is compact, which is to say that any infinite sequence of group elements possesses a limit point belonging to the group manifold.
