Methods for solving relativistic equations in Minkwoski Space with applications in hadronic, nuclear and condensed-matter physics

• Grant number: 13/50027-2
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2013
• End date: May 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Physics - Nuclear Physics
• Agreement: CNRS
• Principal Investigator: Tobias Frederico
• Grantee: Tobias Frederico
• Principal researcher abroad: Jaume Carbonell
• Institution abroad: Université Paris-Sud (Paris 11), France
• Host Institution: Divisão de Engenharia Aeronáutica (IEA). Instituto Tecnológico de Aeronáutica (ITA). Ministério da Defesa (Brasil). São José dos Campos , SP, Brazil
• Associated research grant: 09/00069-5 - Few-body aspects of many-body physics, AP.TEM

Abstract

The main aim of the project is to develop methods for solving the Bethe- Salpeter equation in Minkwoski space, both for bound and scattering states. Two main approaches will be used to derive workable equations: i) direct integration in Minkowski four- dimensional momentum space and ii) the Nakanishi perturbative integral representation of the Bethe-Salpeter amplitudes, which simplify the analytic structure of the kernel. The ladder approximation will be considered, and possibly other two-body irreducible contributions will be included in the kernel. Benchmark calculations will be performed using different methods. It will be considered bound and scattering states of boson-boson, fermion-boson and fermion-fermion systems, in the context of hadronic and nuclear physics, this will enable applications to meson-meson, meson-nucleon and nucleon-nucleon scattering, and possibly to the evaluation of the G-matrix in relativistic models of nuclei. In particular, we will consider effective-field-theory expansion methods for the nuclear interaction and study the matching of relativistic extensions of the Schr odinger equation to the Bethe- Salpeter equation. In condensed-matter physics, the application of the methods developed here will allow the study of exciton states in dopped/deformed grapheme, as well as the transition matrix for the electron-hole states in the continuum. (AU)