arXiv subjects

Christian Grosche

Publications and source records attributed to Christian Grosche.

22 records · Page 2Linked to original sources

arXiv1993

An Introduction into the Feynman Path Integral

In this lecture a short introduction is given into the theory of the Feynman path integral in quantum mechanics. The general formulation in Riemann spaces will be given based on the Weyl- ordering prescription, respectively product ordering prescription, in the quantum Hamiltonian. Also, the theory of space-time transformations and separation of variables will be outlined. As elementary examples I discuss the usual harmonic oscillator, the radial harmonic oscillator, and the Coulomb potential. Lecture given at the graduate college ''Quantenfeldtheorie und deren Anwendung in der Elementarteilchen- und Festkörperphysik'', Universität Leipzig, 16-26 November 1992.

hep-th↗

arXiv1993

Classification of Solvable Feynman Path Integrals

A systematic classification of Feynman path integrals in quantum mechanics is presented and a table of solvable path integrals is given which reflects the progress made during the last ten years or so, including, of course, the main contributions since the invention of the path integral by Feynman in 1942. An outline of the general theory is given. Explicit formulæ for the so-called basic path integrals are presented on which our general scheme to classify and calculate path integrals in quantum mechanics is based.

hep-th↗

arXiv1993

$δ$-Function Perturbations and Boundary Problems by Path Integration

A wide class of boundary problems in quantum mechanics is discussed by using path integrals. This includes motion in half-spaces, radial boxes, rings, and moving boundaries. As a preparation the formalism for the incorporation of $δ$-function perturbations is outlined, which includes the discussion of multiple $δ$-function perturbations, $δ$-function perturbations along perpendicular lines and planes, and moving $δ$-function perturbations. The limiting process, where the strength of the $δ$-function perturbations gets infinite repulsive, has the effect of producing impenetrable walls at the locations of the $δ$-function perturbations, i.e.\ a consistent description for boundary problems with Dirichlet boundary-condition emerges. Several examples illustrate the formalism.

hep-th↗

arXiv1993

Selberg Supertrace Formula for Super Riemann Surfaces III: Bordered Super Riemann Surfaces

This paper is the third in a sequel to develop a super-analogue of the classical Selberg trace formula, the Selberg supertrace formula. It deals with bordered super Riemann surfaces. The theory of bordered super Riemann surfaces is outlined, and the corresponding Selberg supertrace formula is developed. The analytic properties of the Selberg super zeta-functions on bordered super Riemann surfaces are discussed, and super-determinants of Dirac-Laplace operators on bordered super Riemann surfaces are calculated in terms of Selberg super zeta-functions.

hep-th↗