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Nuclear PhysicsB229 (1983) 372-380 ~3North-HollandPublishingCompany
 

Summary: Nuclear PhysicsB229 (1983) 372-380
~3North-HollandPublishingCompany
THE BACKGROUND FIELD METHOD AND THE S-MATRIX
L.F. ABBOTI"1, M.T. GRISARU2 and R.K. SCHAEFER1
Physics Department, Brandeis University, Waltham, MA 02254, USA
Received 26 May 1983
We provethat the S-matrixcan be correctlyobtainedfromthe gauge-invarianteffectiveaction
in the backgroundfieldapproachto gaugetheories. In addition,we present a computationof the
two-loopfermioniccontributionsto the Yang-Mills/3-function.
1. Introduction
It is well established that the background field method [1-6] greatly simplifies
calculations of renormalization factors in gauge theories [4, 7-10]. Less appreciated
is the fact that the method can also be useful for calculating S-matrix elements. The
S-matrix is constructed from trees with vertices and propagators given by the 1PI
Green functions. When constructing these trees, it is sometimes convenient to use
a gauge, which is particularly well suited to the physical process being considered.
This is often a Lorentz non-covariant gauge. In the usual formulation of gauge
theories, the 1PI Green functions must also be computed in this non-covariant
gauge making loop calculations extremely difficult. In the background field approach
the gauge used for calculating 1PI graphs and the gauge used for constructing trees

  

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

 

Collections: Biology and Medicine