1996/10/04 by Oliver Schnetz · 12 citations
Mathematics · Physics and Astronomy · #A priori and a posteriori #Beta function (physics) #Black Holes and Theoretical Physics #Critical dimension #Fixed point #Function (biology) #Functional renormalization group #Mathematical analysis #Mathematical and Theoretical Analysis #Mathematical physics #Mathematics #Numerical methods for differential equations #Physics #Quantum mechanics #Renormalization #Renormalization group #Thermal quantum field theory #hep-th
paper · pdf · doi:10.1063/1.531900
published in Journal of Mathematical Physics 38(2), 738-758 (American Institute of Physics) · 23 pages, LaTeX, AMSsymbols, epsf style, 3 PostScript figures
arxiv created 1996/10/04 · openalex publication_date 1997/02/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
A careful analysis of differential renormalization shows that a distinguished choice of renormalization constants allows for a mathematically more fundamental interpretation of the scheme. With this set of a priori fixed integration constants differential renormalization is most closely related to the theory of generalized functions. The special properties of this scheme are illustrated by application to the toy example of a free massive bosonic theory. Then we apply the scheme to the φ4-theory. The two-point function is calculated up to five loops. The renormalization group is analyzed and the beta-function and the anomalous dimension are calculated up to fourth and fifth order, respectively.