The Behaviours of Gursey Instantons in Phase Space

Abstract

In our previous study, we have investigated the behaviours of spinortype instantons in two-dimensional conformally invariant pure spinor Thirring model in phase space. In this paper, we study the role of the coupling constant in the evolution of the four-dimensional spinor-type instantons in phase space via the Heisenberg ansatz. For this purpose, we consider the Gursey model is a four-dimensional conformally invariant pure spinor model with nonlinear self-coupled spinor term. The model proposed in 1956 as a possible basis for a unitary description of elementary particles (Heisenberg-Bohr dream). This study will also lead us to investigate the dependence of the behaviours of spinor-type instantons in phase space on quantum fractional spinor number as well as dimensions.

Unstable behaviors of classical solutions in spinor-type conformal invariant fermionic models

“…These are presented in Fig.1b and Fig.1c too. As can be seen from Fig.1 (plotted forβ = γ = µ = η = 1), the phase space dynamics of 2-D and 4-D spinor type instantons possess a Duffing oscillator type steady-characterization without forcing and damping [14,20].…”

Common Behaviors of Spinor-Type Instantons in 2D Thirring and 4D Gursey Fermionic Models

“…The solution of GNDES for ( ) 1/3 = 1 is the Gursey instantons given in [4]. Very recently, the role of the coupling constant in the evolution of Gursey instantons in phase space has been investigated [8,9]. For a better understanding of the quantum dynamics of spinor-type instantons in vacuum, the dynamics of Forced Gursey nonlinear differential equation system have been studied [8,16].…”

“…In the ensuing years, Kortel found a class of exact solutions of Gursey spinor wave equation and these were shown to be instantonic and meronic in character [3,4]. After the spinor-type instanton solutions of this model with nonlinear ( ) 4/3 self-coupled spinor term have been found by the spontaneous symmetry breaking of the conformal invariance of , that is, ⟨0| |0⟩ ̸ = 0 [4], many works have been done on this model [5][6][7][8][9]. Gursey model is very important because of the similarity of these solutions to the solutions of pure Yang-Mills theories in four dimensions.…”

The Effect of Bichromatic Potential on Thirring Instantons

“…1, the phase space display of Thirring instantons is given for without potential. As can be seen from Fig.1, the phase space dynamics of 2D spinor type Thirring instantons possess a Duffing oscillator type steady-characterization without forcing and damping [14,15]. It is well known that Duffing oscillator is a famous example describing the motion of a classical particle in a double well potential [25].…”

“…We call these solutions as Thirring instantons. Recently, the role of the coupling constant in the evolution of the two dimensional spinor-type Thirring instantons has been investigated in phase space [14,15]. The vector analysis and orientations of Thirring instantons have been studied [16].…”