A mathematical theory of the Feynman path integral for the generalized Pauli equations. (English) Zbl 1125.81034

Ichinose, Wataru

J. Math. Soc. Japan 59, No. 3, 649-668 (2007).

The present paper,based on the works of C. Groche and F. Steiner [Handbook of Feynman path integrals. Berlin: Springer (1998; Zbl 1029.81045)] and of L. S. Schulman [Techniques and applications of path integration. New York etc.: John Wiley & Sons, Inc. (1981; Zbl 0587.28010)], introduces the Feynman path integral and the phase space Feynman path integral for the generalized Pauli equation. The Feynman path integral is developed from the time-slicing method through broken line paths by considering the stability of Feynman functional integrals over infinitely differentiable functions in \(\mathbb R^n\) by means of the theory of oscillatory integral operators referring to a precedent publication of the author [cf. J. Math. Soc. Japan 55, 957–983 (2003; Zbl 1053.81063)]

Reviewer: Christian Pierre (Louvain-la-Neuve)

MSC:

81S40	Path integrals in quantum mechanics
81S30	Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics
81Q30	Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
81Q05	Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

Keywords:

Feynman path integral; Pauli equation; time-slicing method

Citations:

Zbl 1029.81045; Zbl 0587.28010; Zbl 1053.81063