Equations of Motion and Energy-Momentum 1-Forms for the Coupled Gravitational, Maxwell and Dirac Fields
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A theory where the gravitational, Maxwell and Dirac fields (mathematically represented as particular sections of a convenient Clifford bundle) are treated as fields in Faraday’s sense living in Minkowski spacetime is presented. In our theory we obtain a genuine energy-momentum tensor for the gravitational field and a genuine energy-momentum conservation law for the system of the interacting gravitational, Maxwell and Dirac fields. Moreover, the energy-momentum tensors of the Maxwell and Dirac fields are symmetric, and it is shown that the equations of motion for the gravitational potentials are equivalent to Einstein equation of General Relativity. Precisely, the Einstein equation in which the second member is the sum of the energy-momentum tensors of the Maxwell, Dirac and the interaction Maxwell–Dirac fields all defined in an effective Lorentzian spacetime whose use is eventually no more than a question of mathematical convenience.
KeywordsEnergy-Momentum Tensor Gravitational Fields General Relativity Maxwell Fields Dirac Fields
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- 2.Fernández, V.V., Moya, A.M., Rodrigues, W.A., Jr.: Euclidean clifford algebra. Adv. Appl. Cliff. Algebras 13(Supplement), 1–21 (2001)Google Scholar
- 3.Fernández, V.V., Rodrigues, W.A., Jr.: Gravitation as plastic distortion of the Lorentz vacuum, fundamental theories of physics 168, Springer, Heidelberg. [errata for the book at: http://www.ime.unicamp.br/~126walrod/errataplastic] (2010)
- 5.Grib A.A., Mamamyev S.G., Mostepanenko V.M.: Vacuum quantum effects in strong fields. Friedmann Lab Publ, St Petersburg (1994)Google Scholar
- 6.Guth A.: The Inflationary Universe. Perseus Books, Cambridge (1979)Google Scholar
- 7.Leão, R.F, Rodrigues, W.A., Jr, Wainer, S.A: Concept of lie derivative of spinor fields. A geometrical motivated approach. Adv. Appl. Cliff. Algebras. http://link.springer.com/article/10.1007/s00006-015-0560-y, erratum at http://link.springer.com/article/10.1007/s00006-015-0632-z arXiv:1411.7845v3 [math-ph]
- 8.Helfer, A.D.: Spinor Lie derivatives and Fermion stress-energies. Proc. R. Soc. A (to appear) arXiv:1602.00632 [hep-th]
- 9.Mol, I.: The non-metricity formulation of general relativity. arXiv:1406.0737v2 [physics.gen-ph]
- 15.Rodrigues, W.A. Jr: The nature of the gravitational field and its legitimate energy-momentum tensor. Rep. Math. Phys. 69, 265–279 (2012). arXiv:1109.5272v2 [math-ph]
- 16.Rodrigues, W.A. Jr, Oliveira, E.C.: The many faces of Maxwell, Dirac and Einstein equations. In: A clifford bundle approach (2nd edn.). Lecture notes in physics, pp. 922. A preliminary version of this second edition may be found at http://www.ime.unicamp.br/~walrod/mde062715.pdf (2016)
- 17.Rodrigues, W.A. Jr, Wainer, S.A.: Notes on conservation laws, equations of motion of matter and particle fields in Lorentzian and teleparallel de sitter spacetime structures. Adv. Math. Phys. arXiv:1505.02935v4 [math-ph] (to appear)
- 19.Weinberg S.: Gravitation and Cosmology. Wiley, New York (1972)Google Scholar