Related papers: Multiplicative Renormalization in Causal Perturbat…
$S$-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and…
We briefly review the Hopf algebra structure arising in the renormalization of quantum field theories. We construct the Hopf algebra explicitly for a simple toy model and show how renormalization is achieved for this particular model.
Matrix field theory is a combinatorially non-local field theory which has recently been found to be a non-trivial but solvable QFT example. To generalize such non-perturbative structures to other models, a more combinatorial understanding…
Subdivergences constitute a major obstacle to the evaluation of Feynman integrals and an expression in terms of finite quantities can be a considerable advantage for both analytic and numeric calculations. We report on our implementation of…
In this paper I give an overview of mathematical structures appearing in perturbative algebraic quantum field theory (pAQFT) in the case of the massless scalar field on Minkowski spacetime. I also show how these relate to Kontsevich-Zagier…
We contruct here the Hopf algebra structure underlying the process of renormalization of non-commutative quantum field theory.
The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams…
An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.
A cohomological analysis of the renormalization freedom is performed in the Epstein-Glaser scheme on a flat Euclidean space. We study the deviation from commutativity between the renormalization and the action of all linear partial…
We derive a general formula for renormalized entanglement entropy in even dimensional CFTs holographically dual to Einstein gravity in one dimension higher. In order to renormalize, we adapt the Kounterterm method to asymptotically locally…
I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…
Renormalization-group methods in soft-collinear effective theory are used to perform the resummation of large perturbative logarithms for deep-inelastic scattering in the threshold region x->1. The factorization theorem for the structure…
We study the Connes-Kreimer Hopf algebra of renormalization in the case of gauge theories. We show that the Ward identities and the Slavnov-Taylor identities (in the abelian and non-abelian case respectively) are compatible with the Hopf…
The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings.…
We consider two interacting connected graded Hopf algebras, the former being a comodule-coalgebra on the latter. We show how to define analogues of Connes-Kreimer's renormalization group and Beta function, when the graduation operator is…
We consider a modified form of gravity, which has an extra term quadratic in the Riemann tensor. This term mimics a Yang-Mills theory. The other defining characteristic of this gravity is having the affine connection independent of the…
The dimensionful nature of the coupling in the Einstein-Hilbert action in four dimensions implies that the theory is non-renormalizable; explicit calculation shows that beginning at two loop order, divergences arise that cannot be removed…
We perform a systematic one-loop renormalization of a general renormalizable Yang-Mills theory coupled to scalars and fermions using a regularization scheme with a smooth momentum cutoff $\Lambda$ (implemented through an exponential damping…
In the present work, multiplicative renormalization \cite{dixon} for Yang-Mills theories is reviewed. While this subject is not new, it is suggested that a clear understanding of these methods leads to a systematic way for interpreting the…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…