On the algebra of Dirac bispinor densities: Factorization and inversion theorems

Abstract

The algebraic system formed by Dirac bispinor densities ρi≡ψ̄Γiψ is discussed. The inverse problem - given a set of 16 real functions ρi, which satisfy the bispinor algebra, find the spinor ψ to which they correspond - is solved. An expedient solution to this problem is obtained by introducing a general representation of Dirac spinors. It is shown that this form factorizes into the product of two noncommuting projection operators acting on an arbitrary constant spinor. © 1985 American Institute of Physics.