By N.N. Bogolubov, Anatoly A. Logunov, A.I. Oksak, I. Todorov
Nearly all of the "memorable" result of relativistic quantum idea have been got in the framework of the neighborhood quantum box method. the reason of the fundamental rules of the neighborhood idea and its mathematical constitution has left its mark on all sleek task during this quarter. initially, the axiomatic method arose from makes an attempt to provide a mathematical intending to the quantum box idea of sturdy interactions (of Yukawa type). The fields in this sort of idea are discovered by means of operators in Hilbert area with a favorable Poincare-invariant scalar product. This "classical" a part of the axiomatic process attained its glossy shape way back to the sixties. * It has retained its value even to at the present time, although these days the most clients for the outline of the electro-weak and robust interactions are in reference to the idea of gauge fields. actually, from the viewpoint of the quark version, the idea of robust interactions of Wightman style was once got through proscribing cognizance to simply the "physical" neighborhood operators (such as hadronic fields which includes ''fundamental'' quark fields) appearing in a Hilbert house of actual states. In precept, there are adequate such "physical" fields for an outline of hadronic physics, even if which means one needs to reject the normal neighborhood Lagrangian formalism. (The connection is restored within the approximation of low-energy "phe nomenological" Lagrangians.