Holographic principle and field-to-particle transition formalism in sigma model, dilaton gravity and supergravity: Point particle as end product of field theory and seed of string-brane approach

Abstract

The paper consists of two parts which seem to be independent of each other but at first glance only. In the Part one the field-to-particle transition formalism is applied to the sigma model (string), dilaton gravity and gauged supergravity 0-brane solutions. In addition to the fact that the field-to-particle transition is of interest itself it can be regarded also as the dynamical dimensional reduction which takes into account field fluctuations as well as one can treat it as the method of the consistent quantization in the vicinity of the nontrivial vacuum induced by a field solution. It is shown that in all the cases the end product of the approach is the so-called "non-minimal point particle". In view of this it is conjectured that point particles are not only the end product but also the underlying base of modern high-energy theory even more fundamental than the strings. The Part two is hence devoted to the formal axiomatics of the string-brane approach - there we deepen the above-mentioned conjecture. It turns out that a point particle can be regarded as an extended object from the viewpoint of a macroscopic measurement. The particle is actually observed as the ``cloud'' consisting of the virtual paths and nothing prevents their deviations from the classical trajectory. Therefore, for an observer the real particle can be no more viewed as a point object. However, it cannot be supposed also as a continuous extended object unless we average over all the deviations. Then we obtain the metabrane, which is the composite extended object consisting of the microscopical objects (strings) and cosmological-size ones (3-brane) where the size of a corresponding embedding is governed by the weight constants arising along with the decomposition.