Foundations of Physics

, Volume 40, Issue 11, pp 1681–1699 | Cite as

Spin Path Integrals and Generations

  • Carl BrannenEmail author


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 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 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.


Feynman path integral Mutually unbiased bases Quantum information theory Spin Elementary particles Generations 


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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.RedmondUSA

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