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

The algebraic system formed by Dirac bispinor densities ρ i ≡ψ̄Γ i ψ is discussed. The inverse problem—given a set of 16 real functions ρ i , 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.