Exact relativistic Green’s functions for the time-independent potentials

Abstract

Relativistic formalism of Green's functions is discussed in QCD and QED, where the relativistic Green's functions are constructed using the Schwinger proper time formalism and analysed using the Fock-Feynman-Schwinger method. As a result a simple and exact method is found for the relativistic systems, where the interaction can be written in a time-independent form. In this case one can write the relativistic Green's function as a one-dimensional integral of the corresponding nonrelativistic Green's function. The explicit example for the problem of a charge in the constant magnetic field is discussed in detail, and the exact agreement with the Schwinger relativistic form is demonstrated. A similar analysis is performed in the relativistic Coulomb problem, supporting the accuracy of the proposed relativistic formalism.

Recoupling mechanism for exotic mesons and baryons

“…The subsequent development of this method in [34][35][36] has allowed to understand the nature of the X(3872) [35] and Z b states [36]. For the light quarks this method requires the explicit knowledge of qq spectrum and wave functions, which are available in the QCD string approach [37][38][39][40][41][42][43][44][45][46].…”

“…Since each of h i or H j is a composite system consisting of qq or qqq one must write the corresponding relativistic composite Green's function, using the path integral formalism, see [44][45][46] for a recent review.…”

“…The oscillator parameters for the bottomonium, charmonium and B, D mesons have been obtained in [37][38][39][40][41][42][43][44][45][46], using the expansion of relativistic wave functions, obtained from the solutions of the relativistic string Hamiltonian [49], in the full set of the oscillator wave functions. As a result one obtains…”