FAR AND NEAR ORIGINS OF THE STANDARD MODEL IN PHYSICS OF FUNDAMENTAL INTERACTIONS (TO THE 150TH ANNIVERSARY OF F. KLEIN'S ERLANGEN PROGRAM AND TO THE 100TH ANNIVERSARY OF THE BIRTH OF C. YANG)

In connection with the 150th anniversary of F. Klein’s Erlangen program in geometry and the 100th anniversary of the birth of C. Yang, the main creator, non-Abelian gauge fields are discovered, the far and near sources of the standard in the physics of fundamental models of interactions are concluded. A distant source is the Erlangen program and its subsequent introduction of reaction to relative and classical physics. This material discusses the phenomenon of “inconceivable effectiveness of mathematics in special sciences” (J. Wigner), which becomes clearer on the basis of the “relay model” of the interaction between mathematics and physics proposed by D. Hilbert. The approximation of the Erlangen observation, which is applied to Noether's observations on the connection between meetings and meetings, is considered, as well as the application of the Erlangen observation to the history of physics. It is shown how the extension of this domain to local gauge domains is carried out by C. Yang and R. Millsakoch theories of non-Abelian field gauges (1954), which became a near source on the way to the standard and completed model in 1973-1974.