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The Fourth‐Order Non‐Linear Sigma Models and Asymptotic Freedom in Four Dimensions
Author(s) -
Buchbinder I. L.,
Ketov S. V.
Publication year - 1991
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190390102
Subject(s) - realisation , sigma model , formalism (music) , lagrangian , sigma , mathematical physics , physics , degrees of freedom (physics and chemistry) , mathematics , nonlinear system , quantum mechanics , art , musical , visual arts
Starting with the most general Lagrangian of the fourth‐order non‐linear sigma model in four space‐time dimensions, we calculate the one‐loop, on shell ultra‐violet‐divergent part of the effective action. The formalism is based on the background field method and the generalised Schwinger De Witt technique. The multiplicatively renormalisable case is investigated in some detail. The renormalisation group equations are obtained, and the conditions for a realisation of asymptotic freedom are considered.