  Power duality in Feynman's path integral formulation of quantum mechanics is
investigated. The power duality transformation consists of a change in
coordinate and time variables, an exchange of energy and coupling, and a
classical angular momentum replacement. Two physical systems connected by the
transformation form a power-dual pair. The propagator (Feynman's kernel)
expressed by Feynman's path integral cannot be form-invariant under the
transformation, whereas the promotor constructed by modifying Feynman's path
integral is found form-invariant insofar as the angular momentum is classical.
Upon angular quantization, the power duality breaks down. To save the notion of
power duality, the idea of quasi power duality is proposed, which constitutes
of an ad hoc angular momentum replacement. The power-dual invariant promotor
leads to the quasi-dual invariant Green function. A formula is proposed, which
determines the Green function for one of a dual pair by knowing the Green
function for the other. As examples, the Coulomb-Hooke dual pair and a family
of two-term confinement potentials for a zero-energy state are discussed.
