Equivalence between different classical treatments of the O(N) nonlinear sigma model and their functional Schrödinger equations

A. A. Deriglazov, W. Oliveira, G. Oliveira-Neto

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3 Citations (Scopus)


In this work we derive the Hamiltonian formalism of the O(N) nonlinear sigma model in its original version as a second-class constrained field theory and then as a first-class constrained field theory. We treat the model as a second-class constrained field theory by two different methods: the unconstrained and the Dirac second-class formalisms. We show that the Hamiltonians for all these versions of the model are equivalent. Then, for a particular factor-ordering choice, we write the functional Schrödinger equation for each derived Hamiltonian. We show that they are all identical which justifies our factor-ordering choice and opens the way for a future quantization of the model via the functional Schrödinger representation.

Original languageEnglish
Pages (from-to)755-766
Number of pages12
JournalInternational Journal of Modern Physics A
Issue number5
Publication statusPublished - 20 Feb 2003



  • Constrained systems
  • Dirac formalism
  • Functional Schrödinger representation
  • Sigma model

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Nuclear and High Energy Physics

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