Spin Path Integrals and Generations

TL;DR

This paper explores a novel approach to spin path integrals using mutually unbiased bases, revealing connections to elementary particle generations and implications for lepton masses.

Contribution

It introduces a new framework for spin path integrals based on MUBs and links these to the three generations of elementary particles.

Findings

Spin-1/2 emerges in the long-time limit across three solutions.

The three solutions correspond to the three elementary particle generations.

Applications to lepton mass predictions are discussed.

Abstract

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.