On the construction of QED using ERG

Abstract

It has been known for some time that a smooth momentum cutoff is compatible with local gauge symmetries. In this paper we show concretely how to construct QED using the exact renormalization group (ERG). First, we give a new derivation of the Ward identity for the Wilson action using the technique of composite operators. Second, parameterizing the theory by its asymptotic behavior for a large cutoff, we show how to fine-tune the parameters to satisfy the identity. Third, we recast the identity as invariance of the Wilson action under a non-linear BRST transformation.

18 pages, LaTeX2e; added appendix A to improve sects. 2 and 4; added ref. 12

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• Gauge Invariance, the Quantum Action Principle, and the Renormalization Group
• Ward identities and Wilson renormalization group for QED
• Manifestly Gauge Invariant QCD
• Manifestly gauge invariant QED
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Cited by in corpus (13)

• The nonperturbative functional renormalization group and its applications
• BRST in the Exact RG
• Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations
• Equivalence of Wilson Actions
• BRST invariant RG flows
• Functional flows in QED and the modified Ward-Takahashi identity
• Gauge Invariant Cutoff QED
• Gauge invariant composite operators of QED in the exact renormalization group formalism
• (Non) Gauge Invariance of Wilsonian Effective Actions in (Supersymmetric) Gauge Theories : A Critical Discussion
• Bulk Gauge Fields and Holographic RG from Exact RG
• Background Effective Action with Nonlinear Massive Gauge Fixing
• The generating functional of correlation functions as a high momentum limit of a Wilson action
• Renormalization Group Analysis of a Gursey Model Inspired Field Theory II