Araştırma Makalesi
Yıl 2019,
Cilt: 31 Sayı: 2, 155 - 162, 30.06.2019
Öz
İkinci mertebeden türevlere bağımlı Lagrange
fonksiyonları’nı yeni koordinat tanımlayarak ve/veya Lagrange çarpımı
kullanarak birinci mertebeden türevlere bağımlı hale getirmek mümkündür.
İndirgeme olarak tanımlayacağımız bu süreç için literatürde verilen 3 yöntem
karşılaştırılmıştır. Bu yöntemler ışığında, yozlaşmama şartını sağlayan ikinci
derece Lagrange fonksiyonlarının Hamilton analizi, Dirac-Bergmann metodu
kullanılarak başarılmıştır. Tüm bu teorik inşalara örnek olarak Chern-Simon
teorisi bünyesindeki yozlaşmama şartını sağlayan Chiral salınacı örneği detaylı
olarak incelenmiştir.
Anahtar Kelimeler
: Chiral Salınacı Schmidt metodu İkinci mertebe Lagrange fonksiyonları
Kaynakça
- KAYNAKLARMarsden, J. E. ve Ratiu, T. (1998). Introduction to mechanics ve symmetry: a basic exposition of classical mechanical systems, Springer-Verlag New York.
- Dirac, P.A.M. (1964). Lectures on quantum mechanics, Belfer Graduate School of Science, Monograph Series, Yeshiva University, New york.
- Dirac, P. A. (1958). Generalized hamiltonian dynamics. In Proceedings of the Royal Society of London A: Mathematical, Physical ve Engineering Sciences, 246(1246), 326-332.
- P. G. Bergmann, (1956), Quantization of general covariant field theories, Helv. Phys. Acta, Suppl. 4, 79.
- Gotay, M. J. ve Nester, J. M. (1979). Presymplectic Lagrangian systems. I: the constraint algorithm and the equivalence theorem. In Annales de l’IHP Physique théorique, 30(2) ,129-142.
- Gotay, M. J. ve Nester, J. M. (1980). Generalized constraint algorithm ve special presymplectic manifolds. Geom. Meth. in Math. Phys., Lecture Notes in Mathematics, (775), 78-104.
- Gotay, M. J. Nester, J. M., ve Hinds, G. (1978). Presymplectic manifolds and the Dirac Bergmann theory of constraints. J. Math. Phys., 19(11), 2388-2399
- M. Ostrogradski, (1850), Mem. Acad. St. Petersburg VI, 4 385.
- Çağatay Uçgun F., Esen O. ve Gümral H., (2018), Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians, J. Math. Phys., 59(1).
- Pons J. M., (1989) Ostrogradski's Theorem for Higher-Order Singular Lagrangians, Lett. Math. Phys. 17(3), 181-189.
- Rashid, M. S. ve Khalil, S. S. (1996). Hamiltonian description of higher order lagrangians. Int. J. of Mod. Phys. A, 11(25), 4551-4559.
- Schmidt, H. J. (1994). Stability ve Hamiltonian formulation of higher derivative theories. Phys. Rev. D, 49(12), 6354.
- Schmidt, H. J. (1995). An alternate Hamiltonian formulation of fourth-order theories ve its application to cosmology. e-print arXiv:gr-qc/9501019.
- Esen O. ve Guha P. (2018), On the geometry of the Schmidt-Legendre transformation, J. of Geom. Mec., 10 (3), 251-291.
- J. Lukierski, P. Stichel ve W. Zakrzewski, (1997) Galilean invariant (2 + 1) dimensional models with a Chern-Simons-like term ve D = 2 noncommutative geometry, Ann. Phys. 260, 224-249.
- Cruz M., Gómez-Cortés R., Molgado A. ve Rojas E., (2016), Hamiltonian analysis for linearly acceleration-dependent Lagrangians, J. Math. Phys., 57, 062903
Yıl 2019,
Cilt: 31 Sayı: 2, 155 - 162, 30.06.2019
Öz
Kaynakça
- KAYNAKLARMarsden, J. E. ve Ratiu, T. (1998). Introduction to mechanics ve symmetry: a basic exposition of classical mechanical systems, Springer-Verlag New York.
- Dirac, P.A.M. (1964). Lectures on quantum mechanics, Belfer Graduate School of Science, Monograph Series, Yeshiva University, New york.
- Dirac, P. A. (1958). Generalized hamiltonian dynamics. In Proceedings of the Royal Society of London A: Mathematical, Physical ve Engineering Sciences, 246(1246), 326-332.
- P. G. Bergmann, (1956), Quantization of general covariant field theories, Helv. Phys. Acta, Suppl. 4, 79.
- Gotay, M. J. ve Nester, J. M. (1979). Presymplectic Lagrangian systems. I: the constraint algorithm and the equivalence theorem. In Annales de l’IHP Physique théorique, 30(2) ,129-142.
- Gotay, M. J. ve Nester, J. M. (1980). Generalized constraint algorithm ve special presymplectic manifolds. Geom. Meth. in Math. Phys., Lecture Notes in Mathematics, (775), 78-104.
- Gotay, M. J. Nester, J. M., ve Hinds, G. (1978). Presymplectic manifolds and the Dirac Bergmann theory of constraints. J. Math. Phys., 19(11), 2388-2399
- M. Ostrogradski, (1850), Mem. Acad. St. Petersburg VI, 4 385.
- Çağatay Uçgun F., Esen O. ve Gümral H., (2018), Reductions of topologically massive gravity I: Hamiltonian analysis of second order degenerate Lagrangians, J. Math. Phys., 59(1).
- Pons J. M., (1989) Ostrogradski's Theorem for Higher-Order Singular Lagrangians, Lett. Math. Phys. 17(3), 181-189.
- Rashid, M. S. ve Khalil, S. S. (1996). Hamiltonian description of higher order lagrangians. Int. J. of Mod. Phys. A, 11(25), 4551-4559.
- Schmidt, H. J. (1994). Stability ve Hamiltonian formulation of higher derivative theories. Phys. Rev. D, 49(12), 6354.
- Schmidt, H. J. (1995). An alternate Hamiltonian formulation of fourth-order theories ve its application to cosmology. e-print arXiv:gr-qc/9501019.
- Esen O. ve Guha P. (2018), On the geometry of the Schmidt-Legendre transformation, J. of Geom. Mec., 10 (3), 251-291.
- J. Lukierski, P. Stichel ve W. Zakrzewski, (1997) Galilean invariant (2 + 1) dimensional models with a Chern-Simons-like term ve D = 2 noncommutative geometry, Ann. Phys. 260, 224-249.
- Cruz M., Gómez-Cortés R., Molgado A. ve Rojas E., (2016), Hamiltonian analysis for linearly acceleration-dependent Lagrangians, J. Math. Phys., 57, 062903
Toplam 16 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Araştırma Makaleleri |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Haziran 2019 |
| Yayımlandığı Sayı | Yıl 2019 Cilt: 31 Sayı: 2 |