Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-12-09
Physics
High Energy Physics
High Energy Physics - Theory
17 pages, Proc. of 13th International School & Conference "Foundation & Advances in Nonlinear Science", Eds.: Kuvshinov V.I.,
Scientific paper
Possible quantum mechanical corollaries of changing the vectorial geometrical model of the physical space, extending it twice, in order to describe its spinor structure (in other terminology and emphasis it is known as the Hopf's bundle) are investigated. The extending procedure is realized in cylindrical parabolic coordinates. It is done through expansion twice as much of the domain G so that instead of the half plane (u,v>0) now the entire plane (u,v) should be used accompanied with new identification rules over the boundary points. Solutions of the Klein-Fock and Schrodinger equations are constructed in terms of parabolic cylinder functions. Four types of solutions are possible: \Psi_{++}, \Psi_{--} ; \Psi_{+-}, \Psi_{-+}. The first two \Psi_{++}, \Psi_{--} provide us with single-valued functions of the vectorial space points, whereas last two \Psi_{+-},\Psi_{-+} have discontinuities in the frame of vectorial space and therefore they must be rejected in this model. All four types of functions are continuous ones being regarded in the spinor space. It is established that all solutions \Psi_{++}, \Psi_{--}, \Psi_{+-}, \Psi_{-+} are orthogonal to each other provided that integration is done over extended domain parameterizing the spinor space. Simple selection rules for matric elements of the vector and spinor coordinates, (x,y) and (u,v), respectively, are derived. Selection rules for (u,v) are substantially different in vector and spinor spaces.
No associations
LandOfFree
Space with spinor structure and analytical properties of the solutions of Klein-Fock and Schrodinger equations in cylindric parabolic coordinates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Space with spinor structure and analytical properties of the solutions of Klein-Fock and Schrodinger equations in cylindric parabolic coordinates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Space with spinor structure and analytical properties of the solutions of Klein-Fock and Schrodinger equations in cylindric parabolic coordinates will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-440503