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In the paper Markov Fields by Edward Nelson the introduction section claims that analytically continuing a Markov process with appropriate symmetry properties yields the solution of the Schrodinger equation.

What is the appropriate symmetry required by a Markov process to solve the Schrodinger equation? Is the symmetry that of the Euclidean group?

Furthermore, how would you show a Markov process with appropriate symmetry is a solution to the Schrodinger equation?

Link to the paper: http://www.mathunion.org/ICM/ICM1974.2/Main/icm1974.2.0395.0398.ocr.pdf

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