Common Space of Spin and Spacetime

Details Common Space of Spin and Spacetime Common Space of Spin and Spacetime

2004-09-02

arxiv.org/abs/quant-ph/0409011v4

Found.Phys.Lett. 18 (2005) 243-258

Physics

Quantum Physics

17 pages, a reference corrected, final version published on Foundations of Physics Letters in June of 2005, as a personal trib

Scientific paper

10.1007/s10702-005-6115-z

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.

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