2024/02/02 by Shaoyang Jia, Jia, Shaoyang
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced NMR Techniques and Applications #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nuclear Theory (nucl-th) #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2402.01125
openalex publication_date 2024/02/02 · openalex created_date 2024/02/06 · openalex updated_date 2026/08/01
We propose a method to solve for the pseudoscalar bound state amplitude of a fermion and an antifermion from its Bethe--Salpeter equation (BSE) in the Minkowski space applying spectral representations. With the dressing of the fermion propagators specified by their spectral functions, we first derive the explicit expressions for the Nakanishi spectral functions of the Bethe--Salpeter wave function (BSWF) in terms of these propagators and the Bethe--Salpeter amplitude (BSA) directly from the definition in the momentum space. Applying the rainbow-ladder truncation in the covariant gauge, we then convert the BSE in the momentum space into identities that calculate the spectral functions of the BSA from those of the gauge-boson propagator and of the BSWF. These relations form a closed set of linear functionals for the Nakanishi spectral functions with analytical kernels, laying the foundation for the numerical solution of the BSE in the Minkowski space.