2001/03/16 by M. Koll, Matthias Koll, Koll, Matthias +3
Physics and Astronomy · #Atomic Physics (physics.atom-ph) #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High-Energy Particle Collisions Research #Nuclear Theory (nucl-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-ph #nucl-th #physics.atom-ph
paper · pdf · doi:10.48550/arxiv.nucl-th/0103044
25 pages including 13 figures; revised and extended version
openalex publication_date 2001/03/16 · arxiv created 2001/04/19 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In a general framework that has been labeled the ``gauging of equations method'', we study the diagrams that contribute to Compton scattering off a relativistic composite system. These contributions can be derived for N--particle bound states described by the covariant Bethe--Salpeter equation with a method equivalent to minimal substitution in the one--particle case and yield the correct contributions (including subtraction terms) in the order \cal O(e2). We give the Ward--Takahashi identities for the general two--photon vertex as well as the corresponding constraints for the two--photon irreducible interaction kernel and the Bethe--Salpeter amplitude describing the bound state. From this we can show that gauge invariance holds for the full two--photon vertex. We furthermore study in detail the low--energy limit of the Compton scattering tensor in this approach (including a discussion of the pole terms) and can prove that the full amplitude yields the correct Born--Thomson limit as we shall explicitly show for the spin--0 case. The calculations are completed by the investigation of certain approximations that can be formulated for arbitrary N--particle bound states. We neglect for instance contributions from n--photon irreducible interaction kernels and show that in this case gauge invariance is only realized if either the interaction kernel in the Bethe--Salpeter equation is independent of the total momentum and additionally is of local type, or if the photon energies vanish; furthermore, we find the correct low--energy limit in this approximation. To clarify our approach, we also give the results in the order \cal O (e); as examples, we will quote some resulting lowest order expressions for a q q system explicitly.