Dimensional regularization and renormalization of QED
The tree expansion method of renormalization [see e.g. \textit{G. Gallavotti}, Rev. Mod. Phys. 57, 471-562 (1985)] has been applied to QED by \textit{J. Feldman}, \textit{T. Hurd}, and the authors [QED: A proof of renormalizability. Lect. Notes Phys. 312 (1988)]. The purpose of the present paper is to replace the loop regularization used there, with an x-space formulation of dimensional regularization that is compatible with the tree expansion. Renormalization is achieved by subtraction of Lagrangian counterterms determined through the tree expansion, so does not entail a knowledge of the meromorphic structure of the graph as a function of dimension. This renormalization procedure respects the Ward identities, and the counterterms required are gauge invariant.
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