Wyświetlanie artykułu

The mean acceleration formulas introduced by Nelson in his investigation of links between quantum theory and Markovian diffusions are necessary but insufficient conditions for a unique specification of the process. The resolution of Schrödinger's probabilistic conjecture in terms of Markov-Bernstein processes and the related (induced) dynamical semigroups resolves this problem and sets the uniqueness criteria. We discuss the role of analytic time continuation in this formalism and demonstrate that on the appropriate level of description, the imaginary time transformation executes a mapping between two physically distinct families of Markovian diffusions, both proceeding in real time.