Massive superparticles quantization in cosmological supergravity

In this paper, we investigate geometric quantization of massive superparti- cles in four dimensional space-time which preserves 1 4 of the target space supersymme- try. Because the black holes (also massive black holes) are strong gravitational system, hence, application of such quantization to the supersymmetric cosmological black holes would give us information about quantum gravity. As such supermassive black holes are candidate of dark matter hence our calculations are important from cosmological point of view. The world-line action of this model contains a Wess-Zumino term which breaks d = 4 Lorentz symmetry. We solve Hamiltonian equation and obtain unique solution, which helps to calculate prequantization operator. It yields to corresponding Dirac equation which is important in relativistic quantum mechanics. It will be useful in the second quantization of the same models. On the other hand, superparticles are themselves candidates of dark matter, and dark matter is important for its gravitation eects. Hence, their quantization may yield to quantum gravity theory.