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arXiv:1709.09295 · Foundations of Physics

A Stochastic Version of the Noether Theorem

Alfredo González Lezcano, Alejandro Cabo Montes de

Published May 23, 2018• 5 citations
arXivHTMLPDF
DOI
10.1007/s10701-018-0174-z

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Noether's theorem links the symmetries of a quantum system with its conserved quantities, and is a cornerstone of quantum mechanics. Here we prove a version of Noether's theorem for Markov processes. In quantum mechanics, an observable commutes with the Hamiltonian if and only if its expected value remains constant in time for every state. For Markov processes that no longer hold, but an observable commutes with the Hamiltonian if and only if both its expected value and standard deviation are constant in time for every state. © 2013 American Institute of Physics.