A conformal invariant spinor wave equation with nonlinear couplings has been proposed by Feza Gursey to obtain a unitary description of the elementary particles. The Gursey’s Spinor Model is the only possible conformally invariant spinor model, which contains no derivatives higher than one. Another conformal invariant spinor model is the two-dimensional Thirring Model. We discuss the behaviour of the Gursey instantons in phase space and the role of the coupling constant in the evolution of the Gursey instantons. We compare the behaviour of the Gursey instantons and the Thirring instantons and discuss the similarity between the Gursey and Thirring instantons in phase space.
