New Concept for Studying the Classical and Quantum ThreeBody Problem: Fundamental Irreversibility and Time's Arrow of Dynamical Systems
Abstract
The article formulates the classical threebody problem in conformalEuclidean space (Riemannian manifold), and its equivalence to the Newton threebody problem is mathematically rigorously proved. It is shown that a curved space with a local coordinate system allows us to detect new hidden symmetries of the internal motion of a dynamical system, which allows us to reduce the threebody problem to the 6\emph{th} order system. A new approach makes the system of geodesic equations with respect to the evolution parameter of a dynamical system (\emph{internal time}) \emph{fundamentally irreversible}. To describe the motion of threebody system in different random environments, the corresponding stochastic differential equations (SDEs) are obtained. Using these SDEs, FokkerPlancktype equations are obtained that describe the joint probability distributions of geodesic flows in phase and configuration spaces. The paper also formulates the quantum threebody problem in conformalEuclidean space. In particular, the corresponding wave equations have been obtained for studying the threebody bound states, as well as for investigating multichannel quantum scattering in the framework of the concept of internal time. This allows us to solve the extremely important quantumclassical correspondence problem for dynamical Poincaré systems.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2008.00074
 Bibcode:
 2020arXiv200800074G
 Keywords:

 Mathematical Physics
 EPrint:
 66 pages, 10 figures, 91 references