Abstract
Thirring model 2 boyutlu konformal invaryant saf fermiyonik bir modeldir. Bu modelde Heisenberg yaklaşımı kullanılarak spinör tipi instantonlara karşılık gelen çözümler elde edilmiştir. İnstantonlar standart modelde kuantum alan teorisi bağlamında var olan klasik topolojik çözümlerdir. İnstantonlar farklı vakumlar arasındaki tünellemeye karşılık geldikleri için kuarkların parçacıklar içinde hapsolmasını açıklamada önemli bir rol oynar. Bu çalışmada Thirring modelden yararlanarak elde edilen spinör tipi instanton çözümlerinin dinamiği hakkında daha fazla bilgi elde etmek amaçlanmaktadır. Spinör tipi instanton çözümleri lineer olmayan çözümlerdir. Düzenli ve kaotik hareketi hızlı bir şekilde ayırt edebilmesi ve yarı periyodik hareketin meydana geldiği torusun boyutsallığını belirlemesi Genelleştirilmiş Hizalama İndeksi (Generalized Alignment Index) yöntemini diğer yöntemlere göre öne çıkarmaktadır. Bu çalışmada GALI yöntemi kullanılarak spinör tipi instanton çözümlerinin kaotik davranışı karakterize edilmektedir.
Thanks
Bu taslağı hazırlarken verdiği destek için K. Gediz Akdeniz'e teşekkür ederim. I thank K. Gediz Akdeniz for his support while preparing this manuscript.
References
- Akdeniz, K. G., Smailagic ́, A., 1979. Classical solutions for fermionic models, Il Nuovo Cimento A, vol. 51, no. 3, pp. 345– 357
- Belavin, A.A., Polyakof, A.M., Schwartz, Schwartz, A.S., Tyupkin Yu.S., 1975. Pseudoparticle solutions of Yang-Mills equations, Phys. Lett., B 59 85-87
- Canbaz, B., Onem, C., Aydogmus, F., Akdeniz, K. G., 2012. From Heisenberg ansatz to attractor of Thirring Instanton, Chaos, Solitons & Fractals, vol. 45, no. 2, pp. 188–191
- Christodoulidi, H., Bountis, T.,2006. Low-dimensional quasiperiodic motion in Hamiltonian systems, ROMAI Journal 2, 37-44.
- Dunajski, M., 2010. Solitons, Instantons, and Twistors. Oxford University Press, New York
- Fradkin, E., 2021. Quantum Field Theory: An Integrated Approach. Princeton University Press
- Manos, T., Skokos, Ch., Antonopoulos, Ch., 2012. Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method. Int. J. Bifurcation Chaos 22, 1250218
- Moges, H.T., 2020. Investigating Chaos by the Generalized Alignment Index (GALI) Method Shifman, M.,1994. Instantons in Gauge Theories, World Scientific Publishing Company
- Skokos, Ch., Bountis, T, Antonopoulos, Ch.,2007. Geometrical properties of local dynamics in Hamil- tonian systems: The Generalized Alignment Index (GALI) method, Physica D 231, 30-54
- Skokos, Ch., Bountis, T., 2008. Ch. Antonopoulos. Eur. Phys. J. Spec. Top. 165, 5
- Skokos, Ch., Manos, T., 2016. The Smaller (SALI) and the Generalized (GALI) alignment indices: Efficient methods of chaos detection. Lect. Notes Phys. 915, 129
- Thirring W. E., (1958), A Soluble. Relativistic Field Theory Anal. Phys. 3, 91.
Abstract
The Thirring model is a 2D conformal invariant pure fermionic model. In this model, solutions corresponding to spinor type instantons are obtained by using Heisenberg ansatz. Instantons are classical topological solutions that exist in the context of quantum field theory in the standard model. Since instantons correspond to tunneling between different vacuums, they play an important role in explaining the entrapment of quarks within particles. In this study, it is aimed to get more information about the dynamics of spinor type instanton solutions obtained by using the Thirring model. Spinor-type instanton solutions are non-linear solutions. The ability to quickly distinguish between regular and chaotic motion and determine the dimensionality of the torus in which quasi-periodic motion occurs makes the Generalized Alignment Index method stand out compared to other methods. In this study, the chaotic behavior of spinor-type instanton solutions is characterized using the GALI method.
References
- Akdeniz, K. G., Smailagic ́, A., 1979. Classical solutions for fermionic models, Il Nuovo Cimento A, vol. 51, no. 3, pp. 345– 357
- Belavin, A.A., Polyakof, A.M., Schwartz, Schwartz, A.S., Tyupkin Yu.S., 1975. Pseudoparticle solutions of Yang-Mills equations, Phys. Lett., B 59 85-87
- Canbaz, B., Onem, C., Aydogmus, F., Akdeniz, K. G., 2012. From Heisenberg ansatz to attractor of Thirring Instanton, Chaos, Solitons & Fractals, vol. 45, no. 2, pp. 188–191
- Christodoulidi, H., Bountis, T.,2006. Low-dimensional quasiperiodic motion in Hamiltonian systems, ROMAI Journal 2, 37-44.
- Dunajski, M., 2010. Solitons, Instantons, and Twistors. Oxford University Press, New York
- Fradkin, E., 2021. Quantum Field Theory: An Integrated Approach. Princeton University Press
- Manos, T., Skokos, Ch., Antonopoulos, Ch., 2012. Probing the local dynamics of periodic orbits by the generalized alignment index (GALI) method. Int. J. Bifurcation Chaos 22, 1250218
- Moges, H.T., 2020. Investigating Chaos by the Generalized Alignment Index (GALI) Method Shifman, M.,1994. Instantons in Gauge Theories, World Scientific Publishing Company
- Skokos, Ch., Bountis, T, Antonopoulos, Ch.,2007. Geometrical properties of local dynamics in Hamil- tonian systems: The Generalized Alignment Index (GALI) method, Physica D 231, 30-54
- Skokos, Ch., Bountis, T., 2008. Ch. Antonopoulos. Eur. Phys. J. Spec. Top. 165, 5
- Skokos, Ch., Manos, T., 2016. The Smaller (SALI) and the Generalized (GALI) alignment indices: Efficient methods of chaos detection. Lect. Notes Phys. 915, 129
- Thirring W. E., (1958), A Soluble. Relativistic Field Theory Anal. Phys. 3, 91.
Details
| Primary Language | Turkish |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Early Pub Date | January 30, 2022 |
| Publication Date | January 31, 2022 |
| Published in Issue | Year 2022 Issue: 33 |
