On the topological charge conservation in the three-dimensional O ( 3 ) σ -model.

Jaroslav Dittrich

Aplikace matematiky (1984)

  • Volume: 29, Issue: 5, page 367-371
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Dittrich, Jaroslav. "On the topological charge conservation in the three-dimensional ${\rm O}(3)$$\sigma $-model.." Aplikace matematiky 29.5 (1984): 367-371. <http://eudml.org/doc/15367>.

@article{Dittrich1984,
abstract = {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.},
author = {Dittrich, Jaroslav},
journal = {Aplikace matematiky},
keywords = {field theory},
language = {eng},
number = {5},
pages = {367-371},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the topological charge conservation in the three-dimensional $\{\rm O\}(3)$$\sigma $-model.},
url = {http://eudml.org/doc/15367},
volume = {29},
year = {1984},
}

TY - JOUR
AU - Dittrich, Jaroslav
TI - On the topological charge conservation in the three-dimensional ${\rm O}(3)$$\sigma $-model.
JO - Aplikace matematiky
PY - 1984
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 29
IS - 5
SP - 367
EP - 371
AB - 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.
LA - eng
KW - field theory
UR - http://eudml.org/doc/15367
ER -

References

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  2. A. M. Переломов, Решения типа инстантонов в киральных моделях, Успехи физических наук, 134 (1981), 577-609. (1981) Zbl1170.01413MR0669201
  3. В. А. Фатеев И. В. Фролов А. С. Шварц, Квантовые флуктуации инстантонов в двумерной нелинейной анизотропной σ -модели, Ядерная физика, 32 (1980), 299-300. (1980) Zbl1059.81562
  4. A. Kundu, 10.1016/0370-2693(82)90952-2, Phys. Letters, 110 B (1982), 61 - 63. (1982) MR0647884DOI10.1016/0370-2693(82)90952-2
  5. J. Dittrich, 10.1007/BF01206944, Commun. Math. Phys., 82 (1981), 29-39. (1981) MR0638512DOI10.1007/BF01206944
  6. M. Requardt, 10.1007/BF01208276, Commun. Math. Phys., 80 (1981), 369-379. (1981) Zbl0471.35009MR0626706DOI10.1007/BF01208276
  7. E. Elizalde, 10.1016/0370-2693(80)90671-1, Phys. Letters, 91B (1980), 103-106. (1980) MR0566898DOI10.1016/0370-2693(80)90671-1
  8. L. Schwartz, Analyse mathématique, Hermann, Paris 1967. Chapter VI. (1967) Zbl0171.01301
  9. В. А. Рохлин Д. Б. Фукс, Начальный курс топологии, Геометрические главы. Наука, Москва 1977. (1977) Zbl1225.01071

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