A Cutoff Procedure and Counterterms for Differential Renormalization

Abstract

Explicit divergences and counterterms do not appear in the differential renormalization method, but they are concealed in the neglected surface terms in the formal partial integration procedure used. A systematic real space cutoff procedure for massless ${\varphi }^4$ theory is therefore studied in order to test the method and its compatibility with unitarity. Through 3-loop order, it is found that cutoff bare amplitudes are equal to the renormalized amplitudes previously obtained using the formal procedure plus singular terms which can be consistently cancelled by adding conventional counterterms to the Lagrangian. Renormalization group functions $\beta (g)$ and $\gamma (g)$ obtained in the cutoff theory also agree with previous results.

28 pages, CTP#2099-DTP/92/40-UBECMPF/92/13, 2 figures (not included). (Tex problems solved and information about number of pages and figures added)

References in corpus (5)

• Conformal Symmetry and Differential Regularization of the Three-Gluon Vertex
• Differential Renormalization of Massive Quantum Field Theories
• Differential Renormalization of the Wess-Zumino Model
• A Comment on the Relationship Between Differential and Dimensional Renormalization
• A New Approach to Lower Dimensional Gauge Theories

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• Real versus complex beta-deformation of the N=4 planar super Yang-Mills theory
• Differential Regularization of Chern-Simons-Maxwell Spinor and Scalar Electrodynamics
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• Nonlocal Regularization For Non-Abelian Gauge Theories For Arbitrary Gauge Parameter
• Advances towards the systematization of calculations with Implicit Regularization
• Coordinate space representation for renormalization of quantum electrodynamics