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

J. P. Crawford

doi:10.1063/1.526906

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

J. P. Crawford

Penn State Fayette, The Eberly Campus

Research output: Contribution to journal › Article › peer-review

65 Scopus citations

Abstract

The algebraic system formed by Dirac bispinor densities ρ_i≡ψ̄Γ_iψ 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.

Original language	English (US)
Pages (from-to)	1439-1441
Number of pages	3
Journal	Journal of Mathematical Physics
Volume	26
Issue number	7
DOIs	https://doi.org/10.1063/1.526906
State	Published - Jan 1 1985

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.526906

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abstract = "The algebraic system formed by Dirac bispinor densities ρi≡{\=ψ}Γiψ 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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AB - 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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On the algebra of Dirac bispinor densities: Factorization and inversion theorems

Abstract

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