Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1992-06-26
Annals Phys. 221 (1993) 77-105
Physics
High Energy Physics
High Energy Physics - Phenomenology
28 pages (figures not included)
Scientific paper
10.1006/aphy.1993.1005
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 $\gamma_5$ problems.
Haagensen Peter E.
Latorre Jose I.
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