On the Feynman theory of polarons-a translation of the path integral variational method into a Hamiltonian formalism

Abstract

Feynman's powerful path integral variational method is translated into the language of a Hamiltonian formalism. The lowest energy and the effective mass expressions of Feynman are exactly reproduced in a Hamiltonian language. The author introduces two kinds of subsidiary vector fields, one of which is intended to approximate the true interaction and still be simple enough to be exactly solvable. The other has negative energy and will compensate the effects of the first one approximately.