Potiienko O. Laplace’s method for description of the interference effects in proton-proton scattering and for Monte Carlo event generators.

Thesis is devoted to the development of a method of accounting for theinterference contributions for both the calculations of proton-proton scattering cross sections and the Monte Carlo event generations of inelastic processes using matrix elements method. Although all the calculations are performed within the real scalar phi-3 model, the method can be used for QCD and other gauge theories. The new method of accounting for itnerference contributions is developed. The main idea behind the method is to apply the Laplace’s method not for each of the interference contributions but rather for the sum of contributions with the close maximum points. The method was used to calculate the partial cross-sections andinclusive rapidity distributions with accounting for the final states containing up to 50 secondary particles. The theoretical explanation for the energy dependence of the shape of inclusive rapidity distribution is provided for the first time, considering this dependence exactly as the interference effect. All the corresponding compupational algorithms are also implemented. The new method for Monte Carlo event generations is developed. It is basedon the ideas behind the method of accounting for the interference contributions, which significantly extends the potentials of application of the matrix elements method for the generation of inelastic scattering events. This method makes possible the generation of events with the large number of secondary particles. The new algorithmic method of accounting for the interference effects for generation of inelastic scattering events is developed. The algorithms can be used as the subroutines in existing event generators and cross-section integrators. It is shown that the modulus of the tree diagram amplitude with one incoming particle and an artbitrary number of outgoung particles reaches its maximum at equal four-momenta of the outgoing particles. Taking into account the sum over the permutations of outgoing particles, all this facts leads to the factorial amplification of the coupling. This result differs significantly from the amplification in DGLAP caused by the powers of large logarithm, which evidences about the significance of the phase space region different from that in DGLAP. Thus the new mechanism of the coherence of secondary particles in the showers is established. This mechanism can be taken into account not only for developement of event generations, but also can be used for development of lasers based on new principles. Moreover, the obtained results makes possible generations of the particle showers (parton or hadron, depending on a model) usingthe method of matrix elements. Is is shown that in the processes with formation of multiple showers the significant role is played by the contributions arose from the permutations of secondary particles between showers. It evidences the necessity of accounting for the interference between showers when calculating the cross-sections or generating events. It is shown that the methods proposed in the dissertation can be used for the numerical calculations and events generation for the processes with formation of several multi-particle showers.