Common Space of Spin and Spacetime
Abstract
Given Lorentz invariance in Minkowski spacetime, we investigate a common space of spin and spacetime. To obtain a finite spinor representation of the non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an indefinite inner product space (IIPS) with a normalized positive probability. In this IIPS, the common momentum and common variable of a massive fermion turn out to be ``doubly strict plus-operators''. Due to this nice property, it is straightforward to show an uncertainty relation between fermion mass and proper time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint, and the fermion field equations are derivable from the Lagrangians. Finally, the nonlinear QED equations and Lagrangians are presented as an example.
Cite
@article{arxiv.quant-ph/0409011,
title = {Common Space of Spin and Spacetime},
author = {Wei Min Jin},
journal= {arXiv preprint arXiv:quant-ph/0409011},
year = {2009}
}
Comments
17 pages, a reference corrected, final version published on Foundations of Physics Letters in June of 2005, as a personal tribute to Einstein and Dirac