ar X iv : g r - qc / 0 50 10 56 v 1 1 9 Ja n 20 05 Dynamic quantum theory of large additional dimensions

The Klein-Gordon equation is known in quantum field theory that does not account the changes of space metrics and changes of particles behavior connected with it [1]. Such dynamics is describing by Einsteins equation or Brans-Dicke equation [2]. Wheeler de Witt occupies place of these equations in quantum theory that is generalization of Klein-Gordon equation for the case of general relativity theory and is valid for arbitrary Ryman space [3]. The approach of Wheeler de Witt is applied to brane theory of Universe in paper [4]. However, the variation of bran topology is not accounted in this paper. The variation of space topology is considered in phenomenological way for quantum theory in paper [5]. In paper [6], Wheeler de Witt equation is obtained from priori taken action for inflating brane. In present paper, we will derive equation of Wheeler de Witt type in the framework of brane model with the account of its topology variation in universal space starting from the well-known conservation laws inside brane. It is known that the value p i p i conserves at Lorenz transform where p i is four-dimensional momentum of a particle [7]. With that, the following conservation law p i p i = 0, (1) is valid for non-massive particle. The three-component vector of momentum can be written in non-relativistic quantum mechanics in operator form as − → p = −i¯ h∇. The evident generalization for four-component case is the value p = 1 c H, − → p .