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Stability of Dirac Equation in Four-Dimensional Gravity |
| F. Safari1, H. Jafari1,3**, J. Sadeghi2, S. J. Johnston3, D. Baleanu3,4,5 |
1Department of Mathematics, University of Mazandaran, Babolsar, Iran
2Physics Department, University of Mazandaran, Babolsar 4716-95447, Iran
3Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa
4Department of Mathematics, Faculty of Art and Science, Çankaya University, Balgat 06530, Turkey
5Institute of Space Sciences, Magurele-Bucharest, Romania
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| Cite this article: |
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F. Safari, H. Jafari, J. Sadeghi et al 2017 Chin. Phys. Lett. 34 060301 |
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Abstract We introduce the Dirac equation in four-dimensional gravity which is a generally covariant form. We choose the suitable variable and solve the corresponding equation. To solve such equation and to obtain the corresponding bispinor, we employ the factorization method which introduces the associated Laguerre polynomial. The associated Laguerre polynomials help us to write the Dirac equation of four-dimensional gravity in the form of the shape invariance equation. Thus we write the shape invariance condition with respect to the secondary quantum number. Finally, we obtain the spinor wave function and achieve the corresponding stability of condition for the four-dimensional gravity system.
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Received: 09 January 2017
Published: 23 May 2017
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| PACS: |
03.65.-w
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(Quantum mechanics)
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11.10.Lm
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(Nonlinear or nonlocal theories and models)
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11.30.Na
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(Nonlinear and dynamical symmetries (spectrum-generating symmetries))
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