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Causality and dispersion relations

Causality (Physics). --- Dispersion relations. --- Dispersion relations. Causality (Physics) Potential scattering. --- Potential scattering. --- Nuclear Physics --- Physics --- Physical Sciences & Mathematics --- Causality (Physics) --- Causality --- Nuclear physics --- Quantum theory --- Heisenberg uncertainty principle --- Philosophy --- Dispersion relations --- Potential scattering

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This text offers a brief introduction to the dispersion relations as an approach to calculate S-matrix elements, a formalism that allows one to take advantage of the analytical structure of scattering amplitudes following the basic principles of unitarity and causality. First, the case of two-body scattering is considered and then its contribution to other processes through final-state interactions is discussed. For two-body scattering amplitudes, the general expression for a partial-wave amplitude is derived in the approximation where the crossed channel dynamics is neglected. This is taken as the starting point for many interesting nonperturbative applications, both in the light and heavy quark sector. Subsequently crossed channel dynamics is introduced within the equations for calculating the partial-wave amplitudes. Some applications based on methods that treat crossed-channel dynamics perturbatively are discussed too. The last part of this introductory treatment is dedicated to the further impact of scattering amplitudes on a variety of processes through final-state interactions. Several possible approaches are discussed such as the Muskhelishvili-Omnes dispersive integral equations and other closed formulae. These different formalisms are then applied in particular to the study of resonances presenting a number of challenging properties. The book ends with a chapter illustrating the use of dispersion relations in the nuclear medium for the evaluation of the energy density in nuclear matter.

Dispersion relations. --- Causality (Physics) --- Nuclear physics --- Quantum theory --- Nuclear physics. --- Mathematical physics. --- Quantum theory. --- Nuclear Physics, Heavy Ions, Hadrons. --- Mathematical Methods in Physics. --- Elementary Particles, Quantum Field Theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Atomic nuclei --- Atoms, Nuclei of --- Nucleus of the atom --- Mathematics --- Heavy ions. --- Physics. --- Elementary particles (Physics). --- Quantum field theory. --- Relativistic quantum field theory --- Field theory (Physics) --- Relativity (Physics) --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Ions