Seminar talk, 23 September 2015

From Geometry of Differential Equations
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Speaker: Evgeny Beniaminov

Title: Gauge transformations and the Galileo invariance of the modified Kramers equation for waves processes in the phase space and quantum mechanics

The talk discusses the studies of mathematical models of diffusion scattering of waves in the phase space, and relation of these models with quantum mechanics. We construct a generalized Kramers equation for waves processes in the phase space. It is shown that in these models of classical scattering process of waves, the quantum mechanical description arises as the asymptotic after a small time. In this respect, the proposed models can be considered as examples in which the quantum descriptions arise as approximate ones for certain hypothetical reality.

We show that the proposed models of diffusion scattering of waves possess the property of gauge invariance. This implies that they are described similarly in all inertial coordinate systems, i.e., they are invariant under the Galileo transformations. Thus, in the presented model in experiments it is impossible to determine the velocity of the move of the system relatively to immovable heat medium.

Beniaminov E.M. Scattering of Waves in the Phase Space, Quantum Mechanics, and Irreversibility, EJTP 12, No.32 (2015) 43-60,

Beniaminov E.M. Diffusion Scattering of Waves is a Model of Subquantum Level, EJTP 11, No.30 (2014) 35-48,