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.