Feynman-type integrals defined in terms of general cylindrical approximations

Ph. Combe, R. Rodriguez, Guy Rideau +1 more

Wataru Ichinose

Convergence of a time-slicing approximation is studied in a general way of the Feynman path integral in phase space with an electromagnetic potential. In the present paper a new approximation of the Feynman path integral in phase space, different from the familiar one in physics, is proposed so that its convergence can be shown independently of the choice of electromagnetic potentials and that gauge invariance of the Feynman path integral defined by its limit can be shown directly. It is also shown that the Feynman path integral in phase space defined above can be expressed in the form of the Feynman path integral in configuration space defined in the familiar way in physics, which Feynman himself stated heuristically.

Kh. Namsrai

A. Marchewka, Z. Schuss

Hadjer Bakhti, Ahmed Diaf, Mohammed Hachama

Abstract This paper presents an analytical path-integral treatment of the ℓ -states of an exponential-type potential. We propose a generalization of the Pekeris approximation of the centrifugal term adapted to deformed potentials. To obtain solutions of the radial Feynman Kernel for arbitrary angular number, we perform a nontrivial change of variable accompanied by a local time rescaling. Using Euler angles and the isomorphism between S 3 and SU (2), we convert the radial path integral into a maniable one. Analytical expressions of the energy spectrum and the normalized ℓ -state eigenfunctions are derived from the Green function. Several potentials are obtained as special cases of the general exponential-type potential. Thus, their eigenvalues and eigenfunctions are deduced straightforwardly. Numerical results show that our technique improves the state-of-the-art.

Pavel Exner