Application of the generalized Clifford-Dirac algebra to the proof of the Dirac equation fermi-bose duality

The consideration of the bosonic properties of the Dirac equation with arbitrary mass has been continued. As the necessary mathematical tool the structure and different representations of the 29-dimensional extended real Clifford-Dirac algebra (Phys. Lett. A., 2011, v.375, p.2479) are considered bri...

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Published inTWMS journal of applied and engineering mathematics Vol. 3; no. 1; pp. 46 - 61
Main Authors Simulik, V.M, Krivsky, I. Yu, Lamer, I.L
Format Journal Article
LanguageEnglish
Published Istanbul Turkic World Mathematical Society 01.01.2013
Elman Hasanoglu
Subjects
Algebra
Analysis
Conservation laws
Dirac equation
Duality theory (Mathematics)
Mathematical analysis
Proving
Representations
Symmetry
United States
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Summary:The consideration of the bosonic properties of the Dirac equation with arbitrary mass has been continued. As the necessary mathematical tool the structure and different representations of the 29-dimensional extended real Clifford-Dirac algebra (Phys. Lett. A., 2011, v.375, p.2479) are considered briefly. As a next step we use the start from the Foldy-Wouthuysen representation. On the basis of these two ideas the property of Fermi-Bose duality of the Dirac equation with nonzero mass is proved. The proof is given on the three maim examples: bosonic symmetries, bosonic solutions and bosonic conservation laws. It means that Dirac equation can describe not only the fermionic but also the bosonic states.
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ISSN:2146-1147
2146-1147