The Behaviours of Spinor Type Attractors in Phase Space
A four-dimensional conformal invariant pure spinor wave equation with nonlinear self-coupled spinor term had been proposed in mid-fifties by Feza Gürsey as a possible basis for a unitary description of elementary particles ( Heisenberg-Bohr dream). Gürsey’s Spinor Model is only possible conformally invariant pure spinor model, which contains no derivatives higher than the first. A class of exact solutions Gursey Spinor wave equation has been found by Kortel long ago. The special case of Kortel wave solutions of the Gursey Spinor wave equation was shown to correspond to instantons (Gursey instantons) which reflect the spontaneous symmetry breaking of the conformal invariance by Akdeniz.
Recently, the behaviours of two dimensional spinor type Thirring instantons has been investigated in phase space. In this thesis, we have investigated dynamic characteristics and evolution of Gursey instantons in phase space. We also compared the behaviours of Gursey and Thirring instantons in phase space to understand instanton structure between different quantum spinor number as well as dimensions. Finally we discussed the nonlinear dynamics of Gursey instantons under quantum fluctuation and periodic feedback.
