Abstract
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.
Keywords
References
- 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.
Abstract
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.
Keywords
References
- 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Metrology, Applied and Industrial Physics |
| Journal Section | Fizik / Physics |
| Authors | |
| Publication Date | September 1, 2020 |
| Submission Date | March 10, 2020 |
| Acceptance Date | May 27, 2020 |
| Published in Issue | Year 2020 Volume: 10 Issue: 3 |