Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-01-24
JHEP 0103 (2001) 030
Physics
High Energy Physics
High Energy Physics - Theory
25 pages, 1 figure, minor corrections, some clarifying sentences and references added, version to be published in JHEP 03 (200
Scientific paper
10.1088/1126-6708/2001/03/030
Using the higher covariant derivatives regularization of gauge theories in the framework of the background field method, supplemented with one-loop Pauli-Villars regulator fields, we obtain a version of the renormalization group equation for the regulator fields, whose vacuum energy depends on the background gauge field. It is evaluated using an anomalous Ward-Takahashi identity, which is related to the rescaling anomaly of the auxiliary fields, obtained by the Fujikawa approach. In this way the anomalous origin of the one-loop beta-function in QCD is clearly shown in terms of scaling of effective Lagrangians without the use of any Feynman diagram. The simplicity of the method is due to the preservation of the background and quantum gauge invariance in any step of the calculation.
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