Titlebook: Stochastic Methods and Computer Techniques in Quantum Dynamics; Proceedings of the X H. Mitter (Chairman),L. Pittner Conference proceedings

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978-3-7091-8782-1Springer-Verlag/Wien 1984

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Stochastic Differential Equations,its use as a calculational tool. We also discuss recently developed (matrix) continued fraction methods for solving certain types of stochastic differential equations and their associated Fokker-Planck equation [4–6].

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Feynman Path Integrals,In these lectures I shall present a path integral calculation, starting from a global definition of Feynman path integrals and ending at a scattering cross section formula. Along the way I shall discuss some basic issues which had to be resolved to exploit the computational power of the proposed definition of Feynman integrals.

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The Knife Edge Problem,This paper is a discussion of the semi-classical limit of the propagator in 1 space, 1 time dimension in the case that there is no classical path to expand about.

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Stochastic Quantization and Gauge Fixing in Gauge Theories,These lectures were supposed to focus on a specific non-compact lattice gauge model with a peculiar “stochastic” gauge fixing invented by Zwanziger. But to put this model into perspective I find it appropriate to widen the scope of these lectures somewhat.

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The Heat Kernel on Riemannian Manifolds and Lie Groups,We give exact formulae for the heat Kernel on a class of Riemannian manifolds and Lie groups. These formulae express the heat Kernel in terms of lengths of geodesies of the corresponding manifolds.

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