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

摘要

The paper consists of two parts which seem to be independent of each otherbut at first glance only. In the Part one the field-to-particle transitionformalism is applied to the sigma model (string), dilaton gravity and gaugedsupergravity 0-brane solutions. In addition to the fact that thefield-to-particle transition is of interest itself it can be regarded also asthe dynamical dimensional reduction which takes into account field fluctuationsas well as one can treat it as the method of the consistent quantization in thevicinity of the nontrivial vacuum induced by a field solution. It is shown thatin all the cases the end product of the approach is the so-called "non-minimalpoint particle". In view of this it is conjectured that point particles are notonly the end product but also the underlying base of modern high-energy theoryeven more fundamental than the strings. The Part two is hence devoted to theformal axiomatics of the string-brane approach - there we deepen theabove-mentioned conjecture. It turns out that a point particle can be regardedas an extended object from the viewpoint of a macroscopic measurement. Theparticle is actually observed as the ``cloud'' consisting of the virtual pathsand 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 weaverage over all the deviations. Then we obtain the metabrane, which is thecomposite extended object consisting of the microscopical objects (strings) andcosmological-size ones (3-brane) where the size of a corresponding embedding isgoverned by the weight constants arising along with the decomposition.