Related papers: A note on regularization and renormalization
The partial success of the block renormalization group techniques is analysed in terms of a functional operator which formalizes the idea of self-replicability of a system in terms of smaller blocks which are similar to the original. The…
This paper develops the theory of a sheaf of normal differential operators to a submanifold Y of a complex manifold X as a generalization of the normal bundle. We show that the global sections of this sheaf play an analogous role for formal…
We give an example of infinite order rational transformation that leaves a linear differential equation covariant. This example can be seen as a non-trivial but still simple illustration of an exact representation of the renormalization…
We develop a generalisation of the original theory of regularity structures, [Hai14], which is able to treat SPDEs on manifolds with values in vector bundles. Assume $M$ is a Riemannian manifold and $E\to M$ and $F^i\to M$ are vector…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
The Euclidean renormalization bundle considered in QFT by Connes, Kreimer, and Marcolli has been extended, in a remarkable series of papers by S Agarwala, to Riemannian manifolds $(X,g)$: in particular by the construction of a flat…
It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.
We study the existence of natural and projectively equivariant quantizations for differential operators acting between order 1 vector bundles over a smooth manifold M. To that aim, we make use of the Thomas-Whitehead approach of projective…
A global connection on the Connes Marcolli renormalization bundle relates $\beta$-functions of a class of regularization schemes by gauge transformations, as well as local solutions to $\beta$-functions over curved space-time.
We study differential invariants of linear differential operators and use them to find conditions for equivalence of differential operators acting in line bundles over smooth manifolds with respect to groups of authomorphisms.
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
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…
It is possible to perform some operations with extrafunctions applying these operations separately to each coordinate. Operations performed in this manner are called regular. It is proved that it is possible to extend several operations…
We study the linearization of line bundles and the local structure of actions of connected linear algebraic groups, in the setting of seminormal varieties. We show that several classical results about normal varieties extend to that…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
I review various aspects of Feynman integrals, regularization and renormalization. Following Bloch, I focus on a linear algebraic approach to the Feynman rules, and I try to bring together several renormalization methods found in the…
We exhibit several transformations of surfaces in R^4. First, one that takes a flat surface and gets a surface with flat normal bundle; then, one that takes a surface with flat normal bundle and gets a flat surface; finally, a one-parameter…
We show how a rescaling of fractional operators with bounded kernels may help circumvent their documented deficiencies, for example, the inconsistency at zero or the lack of inverse integral operator. On the other hand, we build a novel…
We introduce two versions of a renormalization group scheme for the equal load sharing fiber bundle model. The renormalization group is based on formulating the fiber bundle model in the language of damage mechanics. A central concept is…
Let M be a manifold endowed with a symmetric affine connection $\Gamma.$ The aim of this paper is to describe a quantization map between the space of second-order polynomials on the cotangent bundle T^{*} M and the space of second-order…