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

Abstract

Relativistic formalism of Green's functions is dicussed in QCD and QED,where the relativistic Green's functions are constructed using the Schwinger proper time formalism and 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 relativistiv Coulomb probem,supporting the accuracy of the proposed relativistic formalism.

arXiv comment24 pages,1 figure,new refs added

References in corpus (28)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• Static quark anti-quark interactions in zero and finite temperature QCD. I. Heavy quark free energies, running coupling and quarkonium binding
• Mass spectra and Regge trajectories of light mesons in the relativistic quark model
• Gauge--invariant field correlators in QCD at finite temperature
• QCD string in light-light and heavy-light mesons
• Rotating QCD string and the meson spectrum
• Nonperturbative corrections to the quark self-energy
• Decay constants of the heavy-light mesons from the field correlator method
• Universal description of radially excited heavy and light vector mesons
• Light-meson orbital excitations in the QCD string approach
• The Feynman-Schwinger representation in QCD
• Determination of Alpha_s(1 GeV) from the charmonium fine structure
• Systematics of quark-antiquark states and scalar exotic mesons
• Strong coupling constant from bottomonium fine structure
• Relativistic path integral and relativistic Hamiltonians in QCD and QED
• Analytic calculation of field-strength correlators
• Spin-dependent interactions in quarkonia
• The quark-gluon Mixed Condensate calculated via Field Correlators
• Field Correlator Method for the confinement in QCD
• Effects of Negative Energy Components in the Constituent Quark Model
• Electromagnetic Scattering from Relativistic Bound States
• The matrix Hamiltonian for hadrons and the role of negative-energy components
• Light 2++ and 0++ mesons
• The sigma meson from QCD sum rules for large-$N_c$ Regge spectra
• QED spectra in the path integral formalism
• Scaling of Dirac Fermions and the WKB approximation
• Mass Formula for Light Nonstrange Mesons and Regge Trajectories in Quark Model
• The linear radial spectrum of scalar mesons within the QCD sum rules in the planar limit

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• Strong decays with the boost-corrected wave functions
• The Relativistic Cornell-type Mechanism of Exotic Scalar Resonances
• Hadron wave functions in high-energy scattering, form factors and strong decays: the effects of the Lorentz contracted form