Related papers: Renormalization and motivic Galois theory
We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac $\delta$-potential -- known to…
The functional renormalisation group equation is derived in a mathematically rigorous fashion in a framework suitable for the Osterwalder-Schrader formulation of quantum field theory. To this end, we devise a very general regularisation…
This paper deals with criteria of algebraic independence for the derivatives of solutions of rank one difference equations. The key idea consists in deriving from the commutativity of the differentiation and difference operators a sequence…
We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue…
On a compact manifold $M$, we consider the affine space $A$ of non self-adjoint perturbations of some invertible elliptic operator acting on sections of some Hermitian bundle, by some differential operator of lower order. We construct and…
Quantum entanglement, a cornerstone of quantum mechanics, remains challenging to classify, particularly in multipartite systems. Here, we present a new interpretation of entanglement classification by revealing a profound connection to…
It is shown that the renormalisation group (RG) equation can be viewed as an equation for Lie transport of physical amplitudes along the integral curves generated by the $\beta$-functions of a quantum field theory. The anomalous dimensions…
We derive norm bounds that imply the convergence of perturbation theory in fermionic quantum field theory if the propagator is summable and has a finite Gram constant. These bounds are sufficient for an application in renormalization group…
We classify the unitary, renormalizable, Lorentz violating quantum field theories of interacting scalars and fermions, obtained improving the behavior of Feynman diagrams by means of higher space derivatives. Higher time derivatives are not…
We show that every linear algebraic group over an algebraically closed field of characteristic zero is the differential Galois group of a regular singular linear differential equation with rational function coefficients.
The requirement that the quantum partition function be invariant under a renormalization group transformation results in a wide class of exact renormalization group equations, differing in the form of the kernel. Physical quantities should…
Random matrices in the large N expansion and the so-called double scaling limit can be used as toy models for quantum gravity: 2D quantum gravity coupled to conformal matter. This has generated a tremendous expansion of random matrix…
Wetterich's equation provides a powerful tool for investigating the existence and universal properties of renormalization group fixed points exhibiting quantum scale invariance. Motivated by recent works on asymptotically safe scalar-tensor…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
Renormalization group method is one of the most powerful tool to obtain approximate solutions to differential equations. We apply the renormalization group method to Hamiltonian systems whose integrable parts linearly depend on action…
We prove that the symmetric monoidal category of mixed motives generated by an abelian variety (more generally, an abelian scheme) can be described as a certain module category. More precisely, we describe it as the category of…
Application of asymptotic freedom to the ultraviolet stability in Euclidean quantum field theories is revisited and illustrated through the hierarchical model making also use of a few technical developments that followed the original works…
We review the use of the exact renormalization group for realization of symmetry in renormalizable field theories. The review consists of three parts. In part I (sects. 2,3,4), we start with the perturbative construction of a renormalizable…
A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…
In recent years, the usual BPHZ algorithm for renormalization in perturbative quantum field theory has been interpreted, after dimensional regularization, as a Birkhoff decomposition of characters on the Hopf algebra of Feynman graphs, with…