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Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors

Yıl 2020, Cilt: 10 Sayı: 3, 1683 - 1691, 01.09.2020
https://doi.org/10.21597/jist.701706

Öz

A compatible spin 1 spinor representation with Clifford algebra (1,3) (or 1,3 Cl ) is derived
for both (1 / 2,1 / 2) and (1, 0) (0,1)  Lorentz group representations with spin 1/2 particles Dirac spinors
in 1,3 Cl . The relation between the two different representations of spin 1 spinors is analogous to the
relation between the electromagnetic vector potential field A and the electromagnetic field strength
tensor F  . From this relationship, the two representations are combined by the formula
u( p, )  ( p, )  p / m. We also note that the Grassmann basis provides more convenient basis for
spin 1 spinors especially in chiral representations of (1, 0) (0,1)  , even though the Clifford basis is more
fitting for spin 1/2 and (1/ 2,1/ 2) spinor representations for both helicity and handedness.

Kaynakça

  • Ashdown MAJ, Somaro SS, Gull SF, Doran CJL, Lasenby AN, 1998. Multilinear Representations of Rotation Groups within Geometric Algebra. Journal of Mathematical Physics, 39(3): 1566-1588.
  • Cartan E, 1938. Leçons sur la theorie des spineurs. Hermann & Cie, Paris.
  • Chisholm JSR, Farwell RS, 1991. Gauge transformations of spinor within a Clifford algebra. Journal of Physics A: Mathematical and General, 32: 2805-2823.
  • Hestenes D, 1975. Observables, operators, and complex numbers in the Dirac theory. Journal of Mathematical Physics, 16(3): 556.
  • Hestenes D, 1986. Clifford algebra and the interpretation of quantum mechanics. In: Chisholm J SR and Common AK, editors, Clifford Algebras and their Applications in Mathematical Physics; Reidel D.
  • Ji C R, Li Z, Suzuki AT, 2015. Electromagnetic gauge field interpolation between the instant form and the front form of the Hamiltonian Dynamics. Physical Review D, 81.
  • Juvet G, 1930. Opérateurs de Dirac et équations de Maxwell. Commentarii Mathematici Helvetici, 2: 225-235.
  • Li Z, An M, Ji CR, 2015. Interpolation Helicity Spinors Between the Instant Form and the Light-front Form. Physical Review D, 92.
  • Lounesto P, 1997. Clifford algebra and Spinors. Cambridge University Press, Cambridge-UK.
  • Pauli W, 1927. Zur Quatenmechanik des magnetischen Elektrons. Zeitschrift fur Physik, 43: 601-623.
  • Pavšič M, 2010. Space inversion of spinors revisited: A possible explanation of chiral behavior in weak interactions. Physics Letters B, 692(3): 212-217.
  • Reisz M, 1947. Sur certain notions fondamentales en théorie quantique relativiste. In: C.R.10 Congrés Math. Scandinaves, Copenhagen; 1946, Jul. Gjellerups Forlag, Copenhagen; 1947. pp. 123-148.
  • Sauter F, 1930. Lösung der Diracschen Gleichungen ohne Spezialisierung der Diracschen Operatoren. Zeitschrift fur Physik, 63: 803-814.
  • Tomonaga S, 1998. The story of spin. University of Chicago Press, p.129, Chicago and London.
  • Winnberg JO, 1977. Superfields as an extension of the spin representation of the orthogonal group. Journal of Mathematical Physics, 18: 625.

Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors

Yıl 2020, Cilt: 10 Sayı: 3, 1683 - 1691, 01.09.2020
https://doi.org/10.21597/jist.701706

Öz

A compatible spin 1 spinor representation with Clifford algebra (1,3) (or 1,3 Cl ) is derived
for both (1 / 2,1 / 2) and (1, 0) (0,1)  Lorentz group representations with spin 1/2 particles Dirac spinors
in 1,3 Cl . The relation between the two different representations of spin 1 spinors is analogous to the
relation between the electromagnetic vector potential field A and the electromagnetic field strength
tensor F  . From this relationship, the two representations are combined by the formula
u( p, )  ( p, )  p / m. We also note that the Grassmann basis provides more convenient basis for
spin 1 spinors especially in chiral representations of (1, 0) (0,1)  , even though the Clifford basis is more
fitting for spin 1/2 and (1/ 2,1/ 2) spinor representations for both helicity and handedness.

Kaynakça

  • Ashdown MAJ, Somaro SS, Gull SF, Doran CJL, Lasenby AN, 1998. Multilinear Representations of Rotation Groups within Geometric Algebra. Journal of Mathematical Physics, 39(3): 1566-1588.
  • Cartan E, 1938. Leçons sur la theorie des spineurs. Hermann & Cie, Paris.
  • Chisholm JSR, Farwell RS, 1991. Gauge transformations of spinor within a Clifford algebra. Journal of Physics A: Mathematical and General, 32: 2805-2823.
  • Hestenes D, 1975. Observables, operators, and complex numbers in the Dirac theory. Journal of Mathematical Physics, 16(3): 556.
  • Hestenes D, 1986. Clifford algebra and the interpretation of quantum mechanics. In: Chisholm J SR and Common AK, editors, Clifford Algebras and their Applications in Mathematical Physics; Reidel D.
  • Ji C R, Li Z, Suzuki AT, 2015. Electromagnetic gauge field interpolation between the instant form and the front form of the Hamiltonian Dynamics. Physical Review D, 81.
  • Juvet G, 1930. Opérateurs de Dirac et équations de Maxwell. Commentarii Mathematici Helvetici, 2: 225-235.
  • Li Z, An M, Ji CR, 2015. Interpolation Helicity Spinors Between the Instant Form and the Light-front Form. Physical Review D, 92.
  • Lounesto P, 1997. Clifford algebra and Spinors. Cambridge University Press, Cambridge-UK.
  • Pauli W, 1927. Zur Quatenmechanik des magnetischen Elektrons. Zeitschrift fur Physik, 43: 601-623.
  • Pavšič M, 2010. Space inversion of spinors revisited: A possible explanation of chiral behavior in weak interactions. Physics Letters B, 692(3): 212-217.
  • Reisz M, 1947. Sur certain notions fondamentales en théorie quantique relativiste. In: C.R.10 Congrés Math. Scandinaves, Copenhagen; 1946, Jul. Gjellerups Forlag, Copenhagen; 1947. pp. 123-148.
  • Sauter F, 1930. Lösung der Diracschen Gleichungen ohne Spezialisierung der Diracschen Operatoren. Zeitschrift fur Physik, 63: 803-814.
  • Tomonaga S, 1998. The story of spin. University of Chicago Press, p.129, Chicago and London.
  • Winnberg JO, 1977. Superfields as an extension of the spin representation of the orthogonal group. Journal of Mathematical Physics, 18: 625.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Metroloji,Uygulamalı ve Endüstriyel Fizik
Bölüm Fizik / Physics
Yazarlar

Murat An 0000-0003-1363-980X

Yayımlanma Tarihi 1 Eylül 2020
Gönderilme Tarihi 10 Mart 2020
Kabul Tarihi 27 Mayıs 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 3

Kaynak Göster

APA An, M. (2020). Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors. Journal of the Institute of Science and Technology, 10(3), 1683-1691. https://doi.org/10.21597/jist.701706
AMA An M. Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors. Iğdır Üniv. Fen Bil Enst. Der. Eylül 2020;10(3):1683-1691. doi:10.21597/jist.701706
Chicago An, Murat. “Spin 1 Spinor Construction With Clifford Algera and Dirac Spin 1/2 Spinors”. Journal of the Institute of Science and Technology 10, sy. 3 (Eylül 2020): 1683-91. https://doi.org/10.21597/jist.701706.
EndNote An M (01 Eylül 2020) Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors. Journal of the Institute of Science and Technology 10 3 1683–1691.
IEEE M. An, “Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors”, Iğdır Üniv. Fen Bil Enst. Der., c. 10, sy. 3, ss. 1683–1691, 2020, doi: 10.21597/jist.701706.
ISNAD An, Murat. “Spin 1 Spinor Construction With Clifford Algera and Dirac Spin 1/2 Spinors”. Journal of the Institute of Science and Technology 10/3 (Eylül 2020), 1683-1691. https://doi.org/10.21597/jist.701706.
JAMA An M. Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors. Iğdır Üniv. Fen Bil Enst. Der. 2020;10:1683–1691.
MLA An, Murat. “Spin 1 Spinor Construction With Clifford Algera and Dirac Spin 1/2 Spinors”. Journal of the Institute of Science and Technology, c. 10, sy. 3, 2020, ss. 1683-91, doi:10.21597/jist.701706.
Vancouver An M. Spin 1 Spinor Construction with Clifford Algera and Dirac Spin 1/2 Spinors. Iğdır Üniv. Fen Bil Enst. Der. 2020;10(3):1683-91.