Self-consistency functional equation in strongly correlated electron systems: a different approach

We propose a new approach to the self-consistency equation, which arises in the problem of the motion of a hole in a quantum antiferromagnet, appropriate to the case of small exchange energy $J$. The functional equation for the Green function is transformed into a differential equation; its solutions are analyzed and compared to the existing numerical calculations. This method allows one to study the limit of $J\to 0$. Application to other strongly correlated electron systems is discussed.