Two-Fermion Bound States within the Bethe-Salpeter Approach

Abstract

To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is suitable for a representation of the vertex functions. We present a numerical algorithm to solve the Bethe-Salpeter equation and investigate in detail the properties of the solution for the scalar, pseudoscalar and vector meson exchange kernels including the stability of bound states. We also compare our results to the non relativistic ones and to the results given by light front dynamics.

32 pages, XIII Tables, 8 figures

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• Solving Bethe-Salpeter equation for two fermions in Minkowski space
• Two-body scattering states in Minkowski space and the Nakanishi integral representation onto the null plane
• Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space
• Analytical properties of the quark propagator from truncated Dyson-Schwinger equation in complex Euclidean space
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• Accounting for the analytical properties of the quark propagator from Dyson-Schwinger equation
• Manifestation of three-body forces in three-body Bethe-Salpeter and light-front equations
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• Mass spectrum of pseudo-scalar glueballs from a Bethe-Salpeter approach with the rainbow-ladder truncation
• Solving the Bethe-Salpeter Equation in Euclidean Space
• Solving the Bethe-Salpeter Equation in Minkowski Space for a Fermion-Scalar system
• Two-fermion Bethe-Salpeter Equation in Minkowski Space: the Nakanishi Way
• Present status of the Bethe-Salpeter approach in Minkowski space
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• Bound states in Yukawa theory
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