Previous |  Up |  Next


field theory
A field of three-component unit vectors on the $2+1$ dimensional spacetime is considered. Two field configurations with different values of the topological charge cannot be connected by the path of field configurations with a finite Euclidean action. Therefore there is no transition between them. The initial and final configurations are assumed to be continuous at infinity. The asymptotic behaviour of intermediate configurations may be arbitrary. The proof is based on the properties of the degree of mapping.
[1] A. M. Perelomov: Instanton-like solutiors in chiral models. Physica, 4D(1981), 1 - 25. MR 0636468
[1b] A. M. Переломов: Решения типа инстантонов в киральных моделях. Успехи физических наук, 134 (1981), 577-609. MR 0669201 | Zbl 1170.01413
[2] В. А. Фатеев И. В. Фролов А. С. Шварц: Квантовые флуктуации инстантонов в двумерной нелинейной анизотропной $\sigma$-модели. Ядерная физика, 32 (1980), 299-300. Zbl 1059.81562
[2b] A. Kundu: Instanton solutions in the anisotropic $\sigma$-model. Phys. Letters, 110 B (1982), 61 - 63. DOI 10.1016/0370-2693(82)90952-2 | MR 0647884
[3] J. Dittrich: Asymptotic behaviour of the classical scalar fields ard topological charges. Commun. Math. Phys., 82 (1981), 29-39. DOI 10.1007/BF01206944 | MR 0638512
[4] M. Requardt: How conclusive is the scaling argument? The conrection between local and global scale variations of finite action solutiors of classical Euler-Lagrange equations. Commun. Math. Phys., 80 (1981), 369-379. DOI 10.1007/BF01208276 | MR 0626706
[5] E. Elizalde: On the topological structure of massive $CP^n$ sigma models. Phys. Letters, 91B (1980), 103-106. DOI 10.1016/0370-2693(80)90671-1 | MR 0566898
[6] L. Schwartz: Analyse mathématique. Hermann, Paris 1967. Chapter VI. Zbl 0171.01301
[7] В. А. Рохлин Д. Б. Фукс: Начальный курс топологии. Геометрические главы. Наука, Москва 1977. Zbl 1225.01071
Partner of
EuDML logo