Bogolyubov–Medvedev–Polivanov S-matrix Method and Its Application to Multi-Particle Systems and in High-Energy Physics

Abstract

The connection between field-theoretic equations based on the Bogolyubov–Medvedev–Polivanov and Lehman–Szymanczyk–Zimmerman $$S$$ -matrix methods is discussed [1]. These equations are used to derive three-dimensional time-ordered relativistic Lippmann–Schwinger-type equations for hadronic collision amplitudes with and without quark degrees of freedom [2, 3]. Quark degrees of freedom are considered following the Huang–Weldon approach [4], in which hadrons are considered as bound states of quarks. Numerical solutions of the obtained equations made it possible to describe well the experimental phase shifts of elastic $$\pi N$$ and $$NN$$ scattering in the low-energy region. Using a separable approximation, a quark–parton model for inclusive production of particles with a large transverse momentum was reproduced [6]. This made it possible to describe the experimental data of inclusive production of a $$\rho $$ meson with a large transverse momentum (≤1.5 GeV/c) in a proton–proton collision in the energy region 2.9 ≤ $$\sqrt s $$ ≤ 64 GeV [5].