Hamiltonian approach to the method of summation over Feynman histories

Abstract

The Feynman method of quantization by summation over q-histories is extended to a summation over q, p-histories, corresponding to the classical variational method of treating q and p as independent variables. The equivalence of this q-p summation to the usual quantization procedure is shown in the Heisenberg picture by choosing convenient canonical coordinates and in the Schrödinger picture by obtaining the usual representations of the q, p operators.