The quenched approximation in some two-dimensional field theories

We investigate the effect of suppressing closed fermion loops (the quenched approximation) in some (1 + 1)-dimensional field theories. In the Schwinger and Thirring models we find that effects of fermion loops on bound state masses can be absorbed in a rescaling of the coupling constant. In the Schwinger model an extra (decoupled) massless ghost appears and the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ becomes infrared divergent. In an extension of the Schwinger model we compute effective lagrangians for the bound state spectrum in the quenched and unquenched case that look rather different.