Abstract
To this purpose, one uses the result that quantum phenomena in the Euclidean formulation of the theory are due to a stochastic space-time background interaction, whose essence is the time derivative of the Wiener process. The problem of calculating both the transition probability, the path integral for the systems of four particles and factorization solution of Fokker-Planck equation are then solved. The transition probability solution of Fokker-Planck equation factorizes into a first component describing the system at its ground state and a second component characterizing its transition dynamics. The path integral for these system are then solved.
Highlights
IntroductionUnderstanding the process of classical Euclidian theory is one of the major challenges in the last twenty years in the fields of Brownian motion dynamics and quantum mechanics
One uses the result that quantum phenomena in the Euclidean formulation of the theory are due to a stochastic space-time background interaction, whose essence is the time derivative of the Wiener process
The transition probability solution of Fokker-Planck equation factorizes into a first component describing the system at its ground state and a second component characterizing its transition dynamics
Summary
Understanding the process of classical Euclidian theory is one of the major challenges in the last twenty years in the fields of Brownian motion dynamics and quantum mechanics. In the Euclidean quantum mechanics (and, in usual quantum mechanics), the quantum nature of the particles can be related, not with the particle itself, but with the stochastic space-time derivative of the Wiener process, used in the right hand side of Jacobi conjugate equation in classic Euclidean mechanics. This explains why these equations become stochastic. In this work we propose to consider another system of stochastic equations equivalent to the previous one and involving the same point of stochastic space-time background for the quantum oscillators as:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
