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Matrix algorithms for solving (in)homogeneous bound state equations.

M Blank1, A Krassnigg

  • 1Institut für Physik, Universität Graz, Universitätsplatz 5, 8010 Graz, Austria.

Computer Physics Communications
|July 16, 2011
PubMed
Summary
This summary is machine-generated.

This study efficiently solves quantum chromodynamics integral equations for hadronic bound states. The inhomogeneous Bethe-Salpeter equation offers advantages for calculating mass spectra, especially for complex systems like baryons.

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Area of Science:

  • * Theoretical Particle Physics
  • * Quantum Chromodynamics
  • * Hadronic Bound State Physics

Background:

  • * Functional approach to quantum chromodynamics (QCD) utilizes covariant integral equations, like the Bethe-Salpeter equation, to study hadronic bound states.
  • * Solving these equations, particularly linear, homogeneous ones, can be computationally intensive, often requiring numerical solutions from other integral equations as input.
  • * Inhomogeneous equations offer a complementary approach to extract off-shell information alongside bound-state properties.

Purpose of the Study:

  • * To demonstrate the efficient numerical solution of both homogeneous and inhomogeneous Bethe-Salpeter equations.
  • * To compare the efficiency and advantages of using the inhomogeneous equation versus the homogeneous equation for calculating hadronic properties.
  • * To provide insights applicable to the study of baryons and other complex multi-quark systems.

Main Methods:

  • * Application of well-established matrix algorithms for eigenvalue problems (homogeneous case).
  • * Utilization of algorithms for solving linear systems (inhomogeneous case).
  • * Numerical solution of both homogeneous and inhomogeneous Bethe-Salpeter equations.

Main Results:

  • * Both homogeneous and inhomogeneous Bethe-Salpeter equations can be solved efficiently using matrix algorithms.
  • * The inhomogeneous equation is found to be as efficient, or even more advantageous, than the homogeneous equation for mass spectrum calculations.
  • * The methodology provides valuable insights for studying baryons and more complex hadronic systems.

Conclusions:

  • * Efficient numerical methods exist for solving covariant integral equations in QCD.
  • * The inhomogeneous Bethe-Salpeter equation presents a powerful and efficient tool for hadronic mass spectrum calculations.
  • * This approach offers significant benefits for theoretical studies of multi-quark systems and beyond.