A Stochastic Version of the Noether Theorem

作者：Gonzalez Lezcano Alfredo; Montes de Oca Alejandro Cabo

来源：Foundations of Physics, 2018, 48(6): 726-746.

DOI：10.1007/s10701-018-0174-z

• Noether theorem
• Stochastic physical models
• Conservation laws
• Stochastic conservation laws
• Hidden variable theories

A stochastic version of the Noether theorem is derived for systems under the action of external random forces. The concept of moment generating functional is employed to describe the symmetry of the stochastic forces. The theorem is applied to two kinds of random covariant forces. One of them generated in an electrodynamic way and the other is defined in the rest frame of the particle as a function of the proper time. For both of them, it is shown the conservation of the mean value of a random drift momentum. The validity of the theorem makes clear that random systems can produce causal stochastic correlations between two faraway separated systems, that had interacted in the past. In addition possible connections of the discussion with the Ives Couder's experimental results are remarked.

• 出版日期2018-6