非线性σ模型

量子场论中,非线性σ模型(nonlinear sigma model) 描述一个纯量场 。M是目标流形。属于閔考斯基時空[1]

定义编辑

若M有黎曼张量 g拉格朗日量[2]

 

O(3)非线性σ模型编辑

 。二维的非线性O(3)模型是

 

其中    

n是 S2→ S2 的函数。第三个同伦群

 

可以将这些函数分类。上文理论的经典解是O(3) 瞬子

参见编辑

参考文献编辑

  1. ^ Gell-Mann, M.; Lévy, M., The axial vector current in beta decay, Il Nuovo Cimento (Italian Physical Society), 1960, 16: 705–726, Bibcode:1960NCim...16..705G, ISSN 1827-6121, doi:10.1007/BF02859738 
  2. ^ Gürsey, F. On the symmetries of strong and weak interactions. Il Nuovo Cimento. 1960, 16 (2): 230–240. Bibcode:1960NCim...16..230G. doi:10.1007/BF02860276. 

外部链接编辑

  • Ketov, S. V. Nonlinear Sigma model页面存档备份,存于互联网档案馆) on Scholarpedia.
  • U. Kulshreshtha, D.S. Kulshreshtha and H.J.W. Mueller-Kirsten, ``Gauge invariant O(N) nonlinear sigma model(s) and gauge invariant Klein-Gordon theory: Wess-Zumino terms and Hamiltonian and BRST formulations``, Helv.Phys.Acta 66 752-794 (1993); U. Kulshreshtha and D.S. Kulshreshtha, ``Front-form Hamiltonian, path integral and BRST formulations of the nonlinear sigma model``, Int. J. Theor. Phys. 41, 1941-1956 (2002), DOI: 10.1023/A:1021009008129.