1996/09/30 by J. L. Jacquot, J.L. Jacquot · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cutoff #Dimensional regularization #Effective action #Fermion #Feynman diagram #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Path integral formulation #Physics #Propagator #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Regularization (linguistics) #Renormalization #hep-th
paper · pdf · doi:10.1103/physrevd.57.6511
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 57(10), 6511-6524 (American Physical Society) · 23 pages, LaTeX, 5 Encapsulated Postscript figures. Improved and revised version, to appear in Phys. Rev. D
arxiv created 1998/02/20 · openalex publication_date 1998/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We regularize in a continuous manner the path integral of QED by the construction of a nonlocal version of its action by means of a regularized form of Dirac's \ensuremathδ functions. Since the action and the measure are both invariant under the gauge group, this regularization scheme is intrinsically nonperturbative. Despite the fact that the nonlocal action converges formally to the local one as the cutoff goes to infinity, the regularized theory keeps trace of the nonlocality through the appearance of a quadratic divergence in the transverse part of the polarization operator. This term which is uniquely defined by the choice of the cutoff functions can be removed by a redefinition of the regularized action. We notice that for chiral fermions on the lattice, there is an obstruction to construct a continuous and nonambiguous regularization in four dimensions. With the help of the regularized equations of motion, we calculate the one particle irreducible functions which are known to be divergent by naive power counting at one loop order.