Abstract
We prove the perturbative renormalizability of Euclidean QED4 using flow equations, i.e. with the aid of the Wilson renormalization group adapted to perturbation theory. As compared toΦ 44 the additional difficulty to overcome is that the regularization violates gauge invariance. We prove that there exists a class of renormalization conditions such that the renormalized Green functions satisfy the QED Ward identities and such that they are infrared finite at nonexceptional momenta. We give bounds on the singular behaviour at exceptional momenta (due to the massless photon) and comment on the adaptation to the case when the fermions are also massless.
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Wilson, K., Kogut, J. B.: The Renormalization Group and the ε-Expansion. Phys. Rep.12C, 75–199 (1974)
Polchinski, J.: Renormalization and Effective Lagrangians. Nucl. Phys.B231, 269–295 (1984)
Keller, G., Kopper, Ch., Salmhofer, M.: Perturbative Renormalization and Effective Lagrangians inΦ 44 . Helv. Phys. Acta65, 32–52 (1991)
Keller, G., Kopper, Ch.: Perturbative Renormalization of Composite Operators via Flow Equations I. Commun. Math. Phys.148, 445–467 (1992)
Keller, G., Kopper, Ch.: Perturbative Renormalization of Composite Operators via Flow Equations II: Short distance expansion. Commun. Math. Phys.153, 245–276 (1993)
Keller, G.: The Perturbative Construction of Symanzik's improved Action forΦ 44 and QED4. Helv. Phys. Acta66, 453 (1993)
Wieczerkowski, C.: Symanzik's Improved actions from the viewpoint of the Renormalization Group. Commun. Math. Phys.120, 148–176 (1988)
Kopper, Ch., Smirnov, V. A.: Analytic Regularization and Minimal Subtraction forΦ 44 with Flow Equations. Z. Phys.C59, 641–645 (1993)
Keller, G.: Local Borel summability of EuclideanΦ 44 : A simple Proof via Differential Flow Equations. Commun. Math. Phys.161, 311–323 (1994)
Tetradis, N., Wetterich, Ch.: Critical exponents from the Average Action. Nucl. Phys.B422, 541–592 (1994)
Ellwanger, U.: Flow equations and Bound states in Quantum Field theory. Z. Phys.C38, 619 (1993); Ellwanger, U., Wetterich, Ch.: Evolution Equations for the Quark Meson Transition. Nucl. Phys.B423, 137–170 (1994)
Tim R. Morris: Derivative Expansion of the Exact Renormalization Group. Phys. Lett.B329, 241–248 (1994); Tetradis, N., Wetterich, Ch.: High Temperature Phase Transitions without Infrared divergences. Int. J. Mod. Phys.A9, 4029–4062 (1994)
Keller, G., Kopper, Ch.: Perturbative Renormalization of QED via flow equations. Phys. Lett.B273, 323–332 (1991)
Keller, G., Kopper, Ch.: Perturbative Renormalization of MasslessΦ 44 with Flow Equations. Commun. Math. Phys.161, 515–532 (1994)
Feldman, J., Hurd, T., Rosen, L., Wright, J.: QED: A proof of Renromalizability. Lecture Notes in Physics, Vol.312, Berlin: Springer 1988
Hurd, T.: Soft Breaking of Gauge Invariance in Regularized Quantum Electrodynamics. Commun. Math. Phys.125, 515–526 (1989)
Rosen, L., Wright, J. D.: Dimensional Regularization and Renormalization of QED. Commun. Math. Phys.134, 433–446 (1990)
Breitenlohner, P., Maison, D.: Dimensionally Renormalized Green's functions for Theories with Massless Particles. Commun. Math. Phys.52, 39–54 (1977); Commun. Math. Phys.52, 55–75 (1977)
Hurd, T.: A Renormalization Prescription for Massless Quantum Electrodynamics. Commun. Math. Phys.120, 469–479 (1989)
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Communicated by D. Brydges
Supported by the Swiss National Science Foundation and by the Ambrose Monell Foundation.
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Keller, G., Kopper, C. Renormalizability proof for QED based on flow equations. Commun.Math. Phys. 176, 193–226 (1996). https://doi.org/10.1007/BF02099368
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DOI: https://doi.org/10.1007/BF02099368