Abstract
We investigate two examples of conformal invariant pure spinor fermionic models, which admit particle-like solutions of the classical field equations. For different dimensions and quantum spinor numbers, the vector field visualizations of the models are constructed to provide a better understanding of the spinor-type instanton dynamics in phase space. The hierarchical cluster analysis method investigations of the models are also presented. Finally, the autocorrelation and power spectrum graphs of models are constructed and frequencies of motions are defined.
Highlights
The success of electron and antielectron interpretation of Dirac’s nonlinear spinor field wave equation brought with itself a great effort among theoretical physicists in searching new nonlinear field equations
The aim of this study is to provide a better understanding to the dynamics of spinortype instanton solutions of fermionic models in phase space for different dimensions and quantum spinor numbers
In this paper we focus on the vector analysis and orientations of Gursey nonlinear differential equation system (GNDES) and Thirring nonlinear differential equation system (TNDES) to provide a better understanding of the behaviors of spinor-type instanton solutions of fermionic models in phase space for different dimensions and quantum spinor numbers
Summary
The success of electron and antielectron (positron) interpretation of Dirac’s nonlinear spinor field wave equation brought with itself a great effort among theoretical physicists in searching new nonlinear field equations. The spinor-type instanton solutions of Thirring model were found via breaking of conformal symmetry and were shown that these solutions were stable [11] This model is simple enough to be analyzed with full details; and yet it contains many of the typical features of the quantization of relativistic quantum field theories [12]. The aim of this study is to provide a better understanding to the dynamics of spinortype instanton solutions of fermionic models in phase space for different dimensions and quantum spinor numbers. For this purpose, the vector fields of conformal invariant pure spinor fermionic models are constructed and their Jacobian determinants are calculated. Hierarchical cluster analysis [14] method investigations of the fermionic models are presented
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