Massive superparticles quantization in cosmological supergravity

In this paper, we investigate geometric quantization of massive superparticles in four dimensional space-time, which preserves $frac{1}{4}$ of the target space supersymmetry. Because the black holes (also massive black holes) are strong gravitational system, hence, application of such quantization to the supersymmetric cosmological blackholes 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 help to calculate prequantization operator. It yields to corresponding Dirac equationwhich is important in relativistic quantum mechanics. It will be useful in the second quantization of the same models. On the other hand superparticles are itself candidate of dark matter and dark matter are important from their gravitation effects, hence their quantization may yields to quantum gravity theory.