General Spin Dirac Equation (II)


In an earlier reading [1], we did demonstrate that one can write down a general spin Dirac equation by modifying the usual Einstein energy-momentum equation via the insertion of the quantity s which is identified with the spin of the particle. That is to say, a Dirac equation that describes a particle of spin where is the normalised Planck constant, σ are the Pauli 2×2 matrices and s=(±1,±2,±3,…,etc.). What is not clear in the reading [1] is how such a modified energy-momentum relation would arise in Nature. At the end of the day, the insertion by the sleight of hand of the quantity s into the usual Einstein energy-momentum equation, would then appear to be nothing more than an idea belonging to the domains of speculation. In the present reading—by making use of the curved spacetime Dirac equations proposed in the work [2], we move the exercise of [1] from the realm of speculation to that of plausibility.

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G. Nyambuya, "General Spin Dirac Equation (II)," Journal of Modern Physics, Vol. 4 No. 8, 2013, pp. 1050-1058. doi: 10.4236/jmp.2013.48141.

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[1] G. G. Nyambuya, Apeiron, Vol. 16, 2009, pp. 516-531.
[2] G. G. Nyambuya, Foundations of Physics, Vol. 38, 2008, pp. 665-677.
[3] P. A. M. Dirac, Proceedings of the Royal Society B: Biological Sciences, Vol. A117, 1928, pp. 610-612.
[4] P. A. M. Dirac, Proceedings of the Royal Society B: Biological Sciences, Vol. A118, 1928, pp. 351-361.
[5] G. G. Nyambuya, “Toward Einstein’s Dream—On a Generalized Theory of Relativity,” LAP LAMBERT Academic Publishing, 2010.
[6] E. Schrodinger, Physical Review, Vol. 28, 1926, pp. 1049-1070. doi:10.1103/PhysRev.28.1049
[7] W. Ratita and J. Schwinger, Physical Review, Vol. 60, 1941, p. 61. doi:10.1103/PhysRev.60.61

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