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A Rigorous Real Time Feynman Path Integral

Ken Loo
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Abstract

Using improper Riemann integrals, we will formulate a rigorous version of the real-time, time-sliced Feynman path integral for the $L^2$ transition probability amplitude. We will do this for nonvector potential Hamiltonians with potential which has at most a finite number of discontinuities and singularities. We will also provide a Nonstandard Analysis version of our formulation.

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Ken Loo. 2000-12-08. A Rigorous Real Time Feynman Path Integral. https://arxiv.org/abs/math-ph/0012014

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