On symmetry in modern physics (dedicated to the 100th anniversary of the birth of academician V.A. Fock)

The development of the gauge symmetry has resulted in a complete determinat ion of the Lagrangians for electromagnetic, weak, strong and gravitational interactions and has created illusions about the construction of "the theor y of everything." However, in just the same way as in classical physics, it became clear that the deductive obtaining of solutions (laws of Nature) is based not only on the principles of the Lagrangian symmetry. To find unamb iguously solutions some additional conditions are needed without which the solutions of the Lagrange equations are ambiguous. The additional condition s such as hypotheses about the integral symmetries of solutions, the bounda ry and initial conditions, the constants entering Lagrangians, and so on ar e essential so that in a number of cases it is possible to construct models (solutions, laws of Nature) without the recourse to the Lagrange method. A n example of using such an approach in one of the rapidly developing domain s of modern physics, namely relativistic nuclear physics, is given. An exac t mathematical language of the gauge symmetry is the differential geometry and that of the additional conditions in the topology, the parameter space properties as a whole. In the present paper the fundamental contribution of V.A. Fock to the development of the concept of space, the primary concept of physics, is given.