You can find in the “Famp pdf” file embedded below a brief presentation of the theoretical background for the calculation of process amplitudes for interactions involving quarks , leptons and gauge bosons, which bosons are the interaction intermediating gluons, as we know in quantum field theory. The computing of amplitudes is based on path integral formalism and we present a way to compute path integrals, known as lattice gauge theory simulation, which assumes, through a so called Wick rotation to imaginary time variable, of the Minkowski space-time to an Euclidean space-time, that we can compute the path integrals based on Euclidean Lagrangian densities, leading to Euclidean action expressions for the quantum electroweak, chromodynamics or unified SU(3)xSU(2)xU(1), grand unified SU(5) gauge theories. The link to a perturbative approach and computation of amplitudes based on Feynman rules for fermions and bosons is also made in the presentation. We find further a succint reminding of the Monte-Carlo sampling method for computing integrals and a wiev of ways to calculate distribution amplitudes, wave functions for mesons and baryons and also effective differential cross sections and decay rates of scattering respective decay processes of hadrons. Finally , can be found the methods to extract, by lattice simulation computing, the effective masses of mesons and baryons and the quark flavour mixing Cabibo-Kobayashi-Maskawa matrix coefficients. Based on the existence of complex phase factors in the Cabibo-Kobayashi-Maskawa coefficients, which leads to CP-violation, the reason why at least three families of quarks must exist in nature is briefly explained. At the end we expose the random walk and mean free path concepts and their application to compute the critical mass of a fissile material for which cross sections of the interaction between the causing fission events neutrons and the fissionable atomic nuclei are known, as computable in a lattice gauge theoretical approach.
This chapter you can also find in the post
Notes on … quantum field theory
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