Solving the Bethe-Salpeter Equation in Euclidean Space

Abstract

Different approaches to solve the spinor-spinor Bethe-Salpeter (BS) equation in Euclidean space are considered. It is argued that the complete set of Dirac matrices is the most appropriate basis to define the partial amplitudes and to solve numerically the resulting system of equations with realistic interaction kernels. Other representations can be obtained by performing proper unitary transformations. A generalization of the iteration method for finding the energy spectrum of the BS equation is discussed and examples of concrete calculations are presented. Comparison of relativistic calculations with available experimental data and with corresponding non relativistic results together with an analysis of the role of Lorentz boost effects and relativistic corrections are presented. A novel method related to the use of hyperspherical harmonics is considered for a representation of the vertex functions suitable for numerical calculations.

19 pages, 7 figures; based on materials of the contribution "Relativistic Description of Two- and Three-Body Systems in Nuclear Physics", ECT*, October 19-13, 2009

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• Three different approaches to the same interaction: the Yukawa model in nuclear physics
• Relative variables of the exact fermion-antifermion bound state wave-function in the Schwinger Model
• Relative energy dependence of the Bethe-Salpeter amplitude in two-dimensional massless QED