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Bosonization of Fermionic Fields and Fermionization of Bosonic Fields

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Abstract

In this paper using the Clifford and spin-Clifford bundles formalism we show how Weyl and Dirac equations formulated in the spin-Clifford bundle may be written in an equivalent form as generalized Maxwell like form formulated in the Clifford bundle. Moreover, we show how Maxwell equation formulated in the Clifford bundle formalism can be written as an equivalent equation for a spinor field in the spin-Cillford bundle. Investigating the details of such equivalences this exercise shows explicitly that a fermionic field is equivalent (in a precise sense) to an equivalence class of well defined boson fields and that a bosonic field is equivalent to a well defined equivalence class of fermionic fields. These equivalences may be called the bosonization of fermionic fields and the fermionization of bosonic fields.

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References

  1. Crumeyrolle, A.: Orthogonal and Symplectic Clifford Algebras. Spinor Structures. Kluwer Academic Publishers, Dordrecht (1990)

    Book  MATH  Google Scholar 

  2. Hestenes, D.: Space-Time Algebra, 2nd revised edn. Birkhäuser, Basel (2015)

  3. Maia Jr., A., Recami, E., Rodrigues Jr., W.A., Rosa, M.A.F.: Magnetic monopoles without string in the Kähler–Clifford algebra bundle: a geometrical interpretation. J. Math. Phys. 31, 502–505 (1990)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Mosna, R.A., Rodrigues Jr., W.A.: The bundles of Algebraic and Dirac–Hestenes spinor fields. J. Math. Phys. 45, 2945–2966 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Rodrigues Jr., W.A.: Algebraic and Dirac–Hestenes spinors and spinor fields. J. Math. Phys. 45, 2908–2994 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Rodrigues Jr., W.A., Capelas de Oliveira, E.: Dirac and Maxwell equations in the Clifford and spin-Clifford bundles. Int. J. Theor. Phys. 29, 397–412 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Rodrigues Jr., W.A., Capelas de Oliveira, E., The Many Faces of Maxwell Dirac and Einstein Equations. A Clifford Bundle Approach, Lecture Notes in Physics 922 (second edition revised and enlarged), Springer, Heidelberg, 2016 (first published as. Lecture Notes in Physics, vol. 722 (2007)

  8. Stratton, J.A.: Electromagnetic Theory. McGraw-Hill Book Co., New York (1941)

    MATH  Google Scholar 

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Correspondence to Waldyr A. Rodrigues Jr..

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Communicated by Rafał Abłamowicz

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Rodrigues, W.A. Bosonization of Fermionic Fields and Fermionization of Bosonic Fields. Adv. Appl. Clifford Algebras 27, 1769–1778 (2017). https://doi.org/10.1007/s00006-017-0762-6

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  • DOI: https://doi.org/10.1007/s00006-017-0762-6

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