A cutoff procedure and counterterms for differential renormalization

1992/06/09 by Daniel Z. Freedman, D. Z. Freedman, K. Johnson +5 · 4 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #Numerical methods for differential equations #hep-th

paper · pdf · doi:10.1016/0550-3213(93)90225-e

published as Nucl.Phys.B395:454-496,1993 · 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)

arxiv created 1992/06/09 · openalex publication_date 1993/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 ϕ⁴ 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 β(g) and γ(g) obtained in the cutoff theory also agree with previous results.

Citations

• A New Approach to Lower Dimensional Gauge Theories
• Integration by parts: The algorithm to calculate β-functions in 4 loops
• A comment on the relationship between differential and dimensional renormalization

Cited by

• Differential regularization of Chern-Simons-Maxwell spinor and scalar electrodynamics
• Constraining differential renormalization in abelian gauge theories
• Holographic normal ordering and multiparticle states in the AdS-CFT correspondence
• Natural renormalization