Spin Path Integrals and Generations

Details Spin Path Integrals and Generations Spin Path Integrals and Generations

2010-06-16

arxiv.org/abs/1006.3114v1

Found.Phys.40:1681-1699,2010

Physics

General Physics

20 pages, 2 figures, accepted at Foundations of Physics

Scientific paper

10.1007/s10701-010-9465-8

The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman \emph{position} path integral can be mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). Since the more common use of MUBs is in finite dimensional Hilbert spaces, this raises the question "what happens when \emph{spin} path integrals are computed over products of MUBs?" Such an assumption makes spin no longer stable. We show that the usual spin-1/2 is obtained in the long-time limit in three orthogonal solutions that we associate with the three elementary particle generations. We give applications to the masses of the elementary leptons.

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