Nonperturbative calculation of the propagator function in a one-dimensional model field theory

The eigenvalue equation of a model one-dimensional Hamiltonian for a given field with self-interaction has been reduced to a second-order difference equation. A Green's operator for the difference equation is introduced and, identifying the one-particle matrix element of the Green's operator as the propagator function for the field, a continued-fraction representation for the propagator is obtained. A generalized continued-fraction form for the n-particle matrix element of the Green's operator is also given

Continued-fraction representation of propagator functions in a Bethe-Salpeter model

Using the well-known relation between the vertex function and the Bethe-Salpeter amplitude and knowledge of the bound-state energy eigenvalues of the Bethe-Salpeter equation, a continued fraction representation for the modified meson propagator DF' is obtained. The Bethe-Salpeter equation for the nucleon-antinucleon problem with a massless-pseudoscalar-meson coupling is solved in a certain approximation, and the corresponding energy eigenvalues are determined through a continued-fraction technique. We have considered the nucleon both as a Dirac particle and also as a scalar particle. The analytic properties of the continued fraction are discussed and the existence of a Lehmann spectral-function representation for the DF' obtained in the approximation is shown

Asymptotic behavior of the pion electromagnetic form factors in Bethe-Salpeter model

Asymptotic behavior of the pion form factors has been discussed treating pion as a bound state of the elementary nucleon and antinucleon system. The matrix-element of the electromagnetic current is written in terms of the Bethe-Salpeter amplitude for the nucleon-antinucleon bound system. Using suitable approximations the Bethe-Salpeter equation for nucleon-antinucleon bound state with nucleons as Dirac spinors has been solved and the corresponding off-shell pion form factors are determined. The form factors are strongly interaction dependent. For coupling g2/16π2 = 15/4 the form factors vanish asymptotically like t-1 and for 14/4 < g2/16π2 < 15/4 the form factors still vanish but less rapidly than t-1