A new type of phase-space path integral

Jean Zinn‐Justin

Lev I. Plimak

Formal structure of phase-space path integrals based on different types of operator orderings is analysed.

Björn Böttcher, Yana A. Butko, René L. Schilling +1 more

This note is devoted to Feynman formulas (i.e., representations of semigroups by limits of n -fold iterated integrals as n → ∞) and their connections with phase space Feynman path integrals. Some pseudodifferential operators corresponding to different types of quantization of a quadratic Hamiltonian function are considered. Lagrangian and Hamiltonian Feynman formulas for semigroups generated by these operators are obtained. Further, a construction of Hamiltonian (phase space) Feynman path integrals is introduced. Due to this construction, the Hamiltonian Feynman formulas obtained here and in our previous papers do coincide with Hamiltonian Feynman path integrals. This connects phase space Feynman path integrals with some integrals with respect to probability measures. These connections enable us to make a contribution to the theory of phase space Feynman path integrals, to prove the existence of some of these integrals, and to study their properties by means of stochastic analysis. The Feynman path integrals thus obtained are different for different types of quantization. This makes it possible to distinguish the process of quantization in the language of Feynman path integrals.

M. Bachmann

Kazuo Takatsuka

A new formalism of the phase-space path integral based on our previously proposed phase-space distribution function is presented. A semiclassical theory for this path integral is also developed. It is shown that the amplitude factor associated with the semiclassical "kernel" is always finite and closely related to Greene's residue, which was devised to predict the occurrence of global chaos in classical systems.

Naoto Kumano‐go, Daisuke Fujiwara