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A Comprehensive Coordinate Space Renormalization of Quantum Electrodynamics to 2-Loop Order

Peter E. Haagensen·Jose I. Latorre
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Abstract

We develop a coordinate space renormalization of massless Quantum Electrodynamics using the powerful method of differential renormalization. Bare one-loop amplitudes are finite at non-coincident external points, but do not accept a Fourier transform into momentum space. The method provides a systematic procedure to obtain one-loop renormalized amplitudes with finite Fourier transforms in strictly four dimensions without the appearance of integrals or the use of a regulator. Higher loops are solved similarly by renormalizing from the inner singularities outwards to the global one. We compute all 1- and 2-loop 1PI diagrams, run renormalization group equations on them and check Ward identities. The method furthermore allows us to discern a particular pattern of renormalization under which certain amplitudes are seen not to contain higher-loop leading logarithms. We finally present the computation of the chiral triangle showing that differential renormalization emerges as a natural scheme to tackle $γ_5$ problems.

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Peter E. Haagensen, Jose I. Latorre. 1992-06-26. A Comprehensive Coordinate Space Renormalization of Quantum Electrodynamics to 2-Loop Order. https://doi.org/10.1006/aphy.1993.1005

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