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Nuclear PhysicsB185(1981) 189-203 :~ North-Holland PublishingCompany
 

Summary: Nuclear PhysicsB185(1981) 189-203
:~ North-Holland PublishingCompany
THE BACKGROUND FIELD METHOD BEYOND ONE LOOP
L. F. ABBOTTI
CERN, Geneva, Switzerland
Received 10November 1980
The background fieldapproach to multi-loopcalculationsin gaugefield theoriesis presented.
A relation between the gauge-invariant effective action computed using this method and the
effectiveaction of the conventionalfunctional approach is derived. Feynman rules are givenand
renormalization is discussed. It is shown that the renormalizationprogramme can be carried out
without any referenceto fieldsappearinginsideloops. Finally,as an explicitexample,the two-loop
contribution to the fl functionof pure Yang-Millstheory is calculatedusing the background field
method.
1. Introduction
Explicit gauge invariance, which is present at the classical level in gauge field
theories, is normally lost when quantum corrections are included. The background
field method [1,2] is a technique which allows one to fix a gauge, and thereby
compute quantum effects, without losing explicit gauge invariance. It thus makes
calculations in gauge theories easier both technically and conceptually. The back-
ground field method is used extensively in analyses of gravity and supergravity and

  

Source: Abbott, Laurence - Center for Neurobiology and Behavior & Department of Physiology and Cellular Biophysics, Columbia University

 

Collections: Biology and Medicine