Finite and Infinitesimal Canonical Transformations

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Abstract
The general relation between the infinitesimal generator of a 1‐parameter subgroup of canonical transformations and the usual finite generating functions is obtained. This relation is found to be simply a generalization of the Hamilton‐Jacobi equation. When the latter relation is solved for the finite generating function, the connections for a finite transformation can be determined without the need for integration of the associated infinitesimal transformation.

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