Despite the century that Einstein's equation, written for the gravitational field, was created, it does not lose its relevance with the discovery of new solutions, and these solutions, in turn, lead to very interesting physical and astrophysical processes in the macro and mega-scientific worlds. . With this in mind, we can say that the equations describing an arbitrary field have a very high probability of finding solutions in a new form, and this reasoning is especially relevant for equations written for the 4th and 5th dimensional fields. The description of the fundamental equation of quantum field theory in the 5-dimensional de Sitter momentum space through the “fundamental mass” M, the creation of computer programs for this equation, the search for new solutions, the comparison with existing experience, and the scientific prediction of future discoveries speak of how relevant this doctoral (PhD) dissertation today.

    Since theoretical physics is a science that studies the objects of the microcosm, the macrocosm and the megaworld, the laws of their interaction on the basis of non-instrumental hypotheses and ideas, then its predictions, including scientific conclusions from new solutions of the fundamental equation, will become a huge factor in the development of all-natural sciences. This is especially true for quarks, gluons and preons in the microcosm, giant astronomical objects in the megaworld, gravitational equations and related objects that will be of practical importance for a more complete description of its basic concepts, solving actual mathematical problems.

    Considering all this, today we have effectively continued our research and published more than 10 scientific articles in republican and foreign publications.

 

Alexander Badalov,

Doctoral student of Samarkand State University.

Scientific adviser - Doctor of Physical and Mathematical Sciences,

Professor Rustam Ibadov.