Abstract
The well-known treatment of the path integral for the Coulomb potential, by means of the Kustaanheimo–Stiefel transformation and a time transformation, is made more transparent by reducing the problem to the equality of two measures on the space of paths. For this equality two proofs are given: an elementary computational one and a short one recurring to general features of stochastic processes. It is shown that the time transformation is a special case of the well-known time change for a continuous local martingale, by which the process is changed to a Brownian motion and which is determined by its quadratic variation.
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