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.
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