Noether’s Theorem: Quantum vs Stochastic

Alfredo González Lezcano, Alejandro Cabo Montes de

Tetsuya Misawa

Quite recently, a symmetric stochastic calculus of variations was proposed to formulate canonical stochastic dynamics, which is an extension of Nelson’s stochastic mechanics. In this article a ‘‘Noether’s theorem’’ is formulated within this calculus of variations. Conservation laws of momentum, angular momentum, and energy are proved, which are related with the same laws in quantum mechanics.

Aubrey Truman, Ian M Davies

J. Martin Lindsay

Tomoi Koide C, Kazuo Tsushima, Takeshi Kodama

We give a pedagogical introduction of the stochastic variational method by considering the quantization of a non-inertial particle system. We show that the effects of fictitious forces are represented in the forms of vector fields which behave analogous to the gauge fields in the electromagnetic interaction. We further discuss that the operator expressions for observables can be defined by applying the stochastic Noether theorem.