The Nambu-Goto action as the one of the quantized space-time excitation

Abstract

The concept of the quantized space-time of the formless finite fundamental elements is suggested. This space-time can be defined as a set of continual space-time coverings by simply connected non-overlapping regions of any form and arbitrary sizes with some probability measure. The functional integrating method and the space-time action problem are analyzed. A string in this space-time is considered as an excitation of a number of fundamental elements forming one-dimensional curve. It is possible to direct the way for the volume term of the space-time action to yield the Nambu-Goto action with this consideration.