Dynamic quantum theory of large additional dimensions for non-massive   particles
  Brane model of universe is considered for zero-mass particle. Equation of Wheeler - de Witt type is obtained using variation principle from the well-known conservation laws inside the brane. This equation includes term accounting the variation of brane topology. Solutions are obtained analytically at some simplifications and the dispersion relations are derived for frequency of wave associated with the particle. 
S.N. Andrianov, V.V. Bochkarev