2000/07/31 by J. Bijtebier
Physics and Astronomy · #Atomic and Molecular Physics #Cold Atom Physics and Bose-Einstein Condensates #Quantum and Classical Electrodynamics #hep-th #nucl-th
paper · pdf · doi:10.1016/s0375-9474(01)01341-0
published as Nucl.Phys. A703 (2002) 327-345 · 16 pages, three figures in one PS file. In this improved version, the writing of the 3D potential is straightforward
arxiv created 2001/06/05 · openalex publication_date 2002/05/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We apply the 3D reduction method we recently proposed for the N-particle Bethe-Salpeter equation to the 4-particle case. We find that the writing of the Bethe-Salpeter equation is not a straightforward task when N is larger or equal to 4, owing to the presence of mutually unconnected interactions, which could lead to an overcounting of some diagrams in the resulting full propagator. We overcome this difficulty in the N=4 case by including three counterterms in the Bethe-Salpeter kernel. The application of our 3D reduction method to the resulting Bethe-Salpeter equation suggests us a modified 3D reduction method, which gives directly the 3D potential, without the need of writing the Bethe-Salpeter kernel explicitly. The modified reduction method is usable for all N.