  The problem of understanding the role of large gauge transformations in
thermal field theories has recently inspired a number of studies of a one
dimensional field theory. Such work has led to the conclusion that gauge
invariance is restored only when the entire perturbation expansion can be
summed. A careful reexamination of that model is shown, h0owever, to lead to
vastly different conclusions when the constraint implied by the field equations
is explicitly taken into account. In particular it is found that none of the
relevant propagators has any temperature dependence and that the effective
action is essentially trivial. A generalization of the model to include bosons
as well as fermions is also solved with qualitatively identical results being
obtained.
