By N.N. Bogolubov, Anatoly A. Logunov, A.I. Oksak, I. Todorov
Nearly all of the "memorable" result of relativistic quantum conception have been received in the framework of the neighborhood quantum box process. the reason of the fundamental ideas of the neighborhood conception and its mathematical constitution has left its mark on all smooth job during this quarter. initially, the axiomatic process arose from makes an attempt to offer a mathematical aspiring to the quantum box concept of robust interactions (of Yukawa type). The fields in this sort of thought are learned by way of operators in Hilbert area with a good Poincare-invariant scalar product. This "classical" a part of the axiomatic procedure attained its glossy shape way back to the sixties. * It has retained its value even to this present day, notwithstanding these days the most customers for the outline of the electro-weak and robust interactions are in reference to the speculation of gauge fields. actually, from the viewpoint of the quark version, the speculation of robust interactions of Wightman sort was once acquired by means of limiting recognition to only the "physical" neighborhood operators (such as hadronic fields inclusive of ''fundamental'' quark fields) performing in a Hilbert house of actual states. In precept, there are adequate such "physical" fields for an outline of hadronic physics, even supposing which means one needs to reject the conventional neighborhood Lagrangian formalism. (The connection is restored within the approximation of low-energy "phe nomenological" Lagrangians.