TL;DR
This paper introduces a refined differential renormalization scheme with fixed constants, linking it to generalized functions, and applies it to phi^4-theory to compute high-order loop corrections and analyze renormalization group properties.
Contribution
It proposes a distinguished choice of renormalization constants that enhances the mathematical foundation of differential renormalization and demonstrates its application to complex quantum field theories.
Findings
Two-point function calculated up to five loops.
Beta-function and anomalous dimension computed to high orders.
Scheme shows improved mathematical consistency.
Abstract
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 phi^4-theory. The two-point function is calculated up to five loops. The renormalization group is analyzed, the beta-function and the anomalous dimension are calculated up to fourth and fifth order, respectively.
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