Soluble model of a single component fermion interacting with a vector meson

Abstract

A model is formulated in two dimensional spacetime in which a massive vector meson is coupled to only the upper or the lower component of the usual two component fermion field operator. This condition implies a unique (nonconserved) V ± A form for the current, a result which is equivalent to the statement that the current is either self-dual or anti-self-dual. The Green's functions of the model are computed using the device of the external source. A significant result which emerges is the fact that the renormalized meson mass is not a polynomial form in the coupling constant, a situation which has not previously occurred in any of the known soluble field theories. Although there is no limit of this model in which one can obtain the Thirring model, it is shown that a particular solution of the latter can be obtained provided that one considers only configurations in which all fermion excitations are moving to the left or all are moving to the right.