Quantum equation of motion for a particle in the field of primordial   fluctuations
  Brane model of universe is considered for a particle. Conservation laws inside the brane are obtained. Equation of motion is derived for a particle using variation principle from these conservation laws. This equation includes terms accounting the variation of brane topology. Its solution is obtained at some approximations and dispersion relation for a particle is derived. 
S.N. Andrianov, V.V. Bochkarev, S.M. Kozyrev