2010Condensed Matter PhysicsOpen access

Fermi-Bose duality of the Dirac equation and extended real Clifford-Dirac algebra

Krivsky, В. М. Симулик

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Abstract

We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2 but also bosons of spin 1.The new bosonic symmetries of the Dirac equation in both the Foldy-Wouthuysen and the Pauli-Dirac representations are found.Among these symmetries (together with the 32-dimensional pure matrix algebra of invariance) the new, physically meaningful, spin 1 Poincar é symmetry of equation under consideration is proved.In order to provide the corresponding proofs, a 64-dimensional extended real Clifford-Dirac algebra is put into consideration.

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We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2 but also bosons of spin 1.The new bosonic symmetries of the Dirac equation in both the Foldy-Wouthuysen and the Pauli-Dirac representations are found.Among these symmetries (together with the 32-dimensional pure matrix algebra of invariance) the new, physically meaningful, spin 1 Poincar é symmetry of equation under consideration is proved.In order to provide the corresponding proofs, a 64-dimensional extended real Clifford-Dirac algebra is put into consideration.

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Available abstract

We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2 but also bosons of spin 1.The new bosonic symmetries of the Dirac equation in both the Foldy-Wouthuysen and the Pauli-Dirac representations are found.Among these symmetries (together with the 32-dimensional pure matrix algebra of invariance) the new, physically meaningful, spin 1 Poincar é symmetry of equation under consideration is proved.In order to provide the corresponding proofs, a 64-dimensional extended real Clifford-Dirac algebra is put into consideration.

Key concepts: Duality (order theory), Dirac algebra, Clifford analysis, Clifford algebra, Dirac (video compression format), Dirac equation, Physics, Mathematical physics

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