Classical solutions of non-linear σ-models and their quantum fluctuations

  • Allan M. Din
Gauge Theories
Part of the Lecture Notes in Physics book series (LNP, volume 135)


I study the properties of O(N) and CPn−1 non-linear σ-MOELS in the two dimensional Euclidean space. All classical solutions of the equations of motion can be characterized and in the CPn−1 model they can be expressed in a simple and explicit way in terms of holomorphic vectors. The topological winding number and the action of the general CPn−1 solution can be evaluated and the latter turns out always to be an integer multiple of 2π. I further discuss the stability of the solutions and the problem of one-loop calculations of quantum fluctuations around classical solutions.


Classical Solution Quantum Fluctuation Dimensional Euclidean Space Instanton Solution Finite Action 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Allan M. Din
    • 1
  1. 1.Laboratoire d'Annecy de Physique des ParticulesAnnecy-le-VieuxFrance

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