Summary
We solve the heat equation associated with a Schrödinger operator with magnetic field onR d using a stochastic integral which involves only the magnetic field and does not use any potential of the field. Then we study a particular case on the torusT d to show that our formula is no longer true and that an hypothesis like simple connexity is necessary.
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Prat, J.J. Résolution de l'équation de Schrödinger par intégration stochastique du champ magnétique. Probab. Th. Rel. Fields 95, 217–235 (1993). https://doi.org/10.1007/BF01192271
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DOI: https://doi.org/10.1007/BF01192271