. ge n - ph ] 9 A ug 2 00 9 Spin Path Integrals and Generations
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چکیده
Two consecutive measurements of the position of a non relativistic free particle will give entirely unrelated results. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have explained this property of position observables as a result of a path in the Feynman integral being mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). On the other hand, two consecutive measurements of a particle's spin give identical results. This raises the question " what happens when spin path integrals are computed over products of MUBs? " We show that the usual Pauli spin is obtained in the long time limit along with three generations of particles. We propose applications to the masses and mixing matrices of the elementary fermions.
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