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Physics  2000 

A Rigorous Real Time Feynman Path Integral

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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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