Perturbative construction of the two-dimensional O(N) nonlinear sigma model with ERG

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LÜTFÜOĞLU B. C., Sonoda H.

TURKISH JOURNAL OF PHYSICS, cilt.41, sa.3, ss.244-261, 2017 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 3
  • Basım Tarihi: 2017
  • Doi Numarası: 10.3906/fiz-1701-5
  • Dergi Adı: TURKISH JOURNAL OF PHYSICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.244-261
  • Anahtar Kelimeler: Exact renormalization group, nonlinear sigma models, RENORMALIZATION, DIMENSIONS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We use the exact renormalization group (ERG) perturbatively to construct the Wilson action for the two-dimensional O(N) nonlinear sigma model (NLSM). The construction amounts to regularization of a nonlinear symmetry with a momentum cutoff. We find out that the model is parameterized by three functions. We show how to tune them by imposing the Ward-Takahashi (WT) identity. We construct two composite operators that generate infinitesimal change of the coupling constant and the renormalization of the scalar fields. Finally we show how the beta functions and the anomalous dimensions arise in the model up to 1-loop.