Hard-Soft Renormalization and the Exact Renormalization Group

Abstract

The Wilsonian exact renormalization group gives a natural framework in which ultraviolet and infrared divergences can be treated separately. In massless QED we introduce, as the only mass parameter, a renormalization scale ${Ł}_R>0$. We prove, using the flow equation technique, that infrared convergence is a necessary consequence of any zero-momentum renormalization condition at ${Ł}_R$ compatible with the effective Ward identities and axial symmetry. The same formalism is applied to renormalize gauge-invariant composite operators and to prove their infrared finiteness; in particular we consider the case of the axial current operator and its anomaly.

20 pages, RevTex; changes in Abstract, Introduction and Conclusions; Note added in proof; to be published in Nucl.Phys.B

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