Related papers: Renormalization and motivic Galois theory
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
Matrix models of 2D quantum gravity are either exactly solvable for matter of central charge $ c\leq 1, $ or not understood. It would be useful to devise an approximate scheme which would be reasonable for the known cases and could be…
We construct a general renormalization group transformation on quantum states, independent of any Hamiltonian dynamics of the system. We illustrate this procedure for translational invariant matrix product states in one dimension and show…
Let T be a Tannakian category over a field k of characteristic 0 and \pi(T) its fundamental group. In this paper we prove that there is a bijection between the otimes-equivalence classes of Tannakian subcategories of T and the normal affine…
We study the \'{e}tale fundamental groups of singular reduced connected curves defined over an algebraically closed field of arbitrary prime characteristic. It is shown that when the curve is projective, the \'{e}tale fundamental group is a…
We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge…
The Kadanoff-Wilson renormalization group approach for a scalar self-interacting field theor generally coupled with gravity is presented. An average potential that monitors the fluctuations of the blocked field in different scaling regimes…
A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…
The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…
Recently there has been much effort in developing a quantum generalisation of reference frame transformations. Despite important progress, a complete understanding of their principles is still lacking. In particular, we argue that previous…
Two very different problems that can be studied by renormalization group methods are discussed with the aim of showing the conceptual unity that renormalization group has introduced in some areas of theoretical Physics. The two problems…
We present a renormalization group (RG) approach to explain universal features of extreme statistics, applied here to independent, identically distributed variables. The outlines of the theory have been described in a previous Letter, the…
An elementary introduction to perturbative renormalization and renormalization group is presented. No prior knowledge of field theory is necessary because we do not refer to a particular physical theory. We are thus able to disentangle what…
A regularization renormalization method ($RRM$) in quantum field theory ($QFT$) is discussed with simple rules: Once a divergent integral $I$ is encountered, we first take its derivative with respect to some mass parameter enough times,…
We consider random Hermitian matrices made of complex or real $M\times N$ rectangular blocks, where the blocks are drawn from various ensembles. These matrices have $N$ pairs of opposite real nonvanishing eigenvalues, as well as $M-N$ zero…
The asymptotic high momentum behaviour of quantum field theories with cubic interactions is investigated using renormalization group techniques in the asymmetric limit x << 1. Particular emphasis is paid to theories with interactions…
We give a universal construction of a derived affine group scheme and its representation category from a symmetric monoidal infinity-category, which we shall call the tannnakization of a symmetric monoidal infinity-category. This can be…
We discuss the following proposition: Renormalization Group flow of quantum theory with a biased symmetry exhibits a fixed hypersurface at which the symmetry is exact. Such emergent symmetries may have important phenomenological…
We tackle the issue of renormalizability for Tensorial Group Field Theories (TGFT) including gauge invariance conditions, with the rigorous tool of multi-scale analysis, to prepare the ground for applications to quantum gravity models. In…
To unify the quantum electrodynamics (QED) under the first principle which brings the renormalization unartificially, we study Feynman diagrams in QED according to the set theory and the category theory. We add the restriction on the…