Common space of spin and spacetime

摘要

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 (lips) with a normalized positive probability. In this lips, 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 lips, 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.