Effective Action

Part of the Theoretical and Mathematical Physics book series (TMP)

Abstract

This Chapter introduces the notion of an effective action for a quantum field theory. The effective action is defined as a functional whose variations over classical backgrounds yield averages of operators (such as currents, stress-energy tensors and etc.). The arguments which lead to this definition are straightforward for non-interacting quantum fields. The effective action can then be defined by the Ray-Singer formula provided that one uses Laplace-type operators. This implies a ‘Euclidean’ formulation of the theory. To meet these requirements the analysis, after a short overview of statistical mechanics, is applied to finite-temperature field theories. The aim of the present Chapter is basically to show how the spectral geometry methods can be used to reproduce a number of known QFT results, usually derived with the help of Feynman diagrams. Among them are one-loop effective (Coleman-Weinberg) potential and beta functions in gauge theories. The material also includes the following topics: relation between the Euclidean effective action and partition functions, complex geometries, renormalization theory, properties of the effective action of gauge fields, Faddeev-Popov ghosts, and the asymptotic freedom in quantum chromodynamics.

Keywords

Gauge Theory Partition Function Effective Action Classical Action Feynman Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Dubna International UniversityDubnaRussia
  2. 2.CMCCUniversidade Federal do ABCSanto AndreBrazil

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