The role of initial conditions in presence of extra dimensions

Quantum field theory in (4+1)-dimensional bulk space with boundary, representing a 3-brane, is considered. We study the impact of the initial conditions in the bulk on the field dynamics on the brane. We demonstrate that these conditions determine the Kaluza–Klein measure. We also establish the existence of a rich family of quantum fields on the brane, generated by the same bulk action, but corresponding to different initial conditions. A simple classification of these fields is proposed and it is shown that some of them lead to ultraviolet finite theories, which have common features with strings.