Related papers: On Renormalization Group in Abstract QFT
The functional renormalization group (FRG), an established computational method for quantum many-body phenomena, has been subject to a diversification in topical applications, analytic approximations and numerical implementations. Despite…
The recently developed gauge-invariant formalism for the treatment of fluctuations in holographic renormalization group (RG) flows overcomes most of the previously encountered technical difficulties. I summarize the formalism and present…
Normalizing flows leverage the Change of Variables Formula (CVF) to define flexible density models. Yet, the requirement of smooth transformations (diffeomorphisms) in the CVF poses a significant challenge in the construction of these…
We consider the coarse-graining of holographic quantum error correcting codes under a generalized notion of bulk renormalization-group flow. In particular, we study the renormalization under this flow of the $A/4G$ term in the…
Two-loop Feynman integrals of the massive $\phi^4_d$ field theory are explicitly obtained for generic space dimensions $d$. Corresponding renormalization-group functions are expressed in a compact form in terms of Gauss hypergeometric…
First, we reformulate RG transformations in a recursive way with introduction of an order-parameter field. As a result, we manifest the RG flow of an effective field theory through the emergence of an extra dimensional space, where both RG…
We discuss the effect of wave function renormalization (WFR) in asymptotically safe gravity. We show that there are two WFR-invariant quantities, and the renormalization (RG) equations may be written entirely in terms of these quantities.…
We review recent developments in the theory of renormalisation group flows in minimal models with boundaries. Among these, we discuss in particular the perturbative calculations of Recknagel et al, not only as a tool to predict the IR…
We combine old ideas about exact renormalization-group-flow (RGF) equations with the Vilkovisky-De Witt (VDW) approach to reparametrization invariant effective actions and arrive at a new, exact, gauge-invariant RGF equation. The price to…
We study the holographic renormalization group (RG) flow triggered by a classically marginal operator. When a marginal operator deforms a conformal field theory, it does not yield a nontrivial renormalization group flow at the classical…
We discuss a two-parameter renormalization group (RG) consideration of a phyllotaxis model in the framework of the ``energetic approach'' proposed by L. Levitov in 1991. Following L. Levitov, we consider an equilibrium distribution of…
These lecture notes provide a pedagogical introduction to a specific continuum implementation of the Wilsonian renormalization group, the effective average action. Its general properties and, in particular, its functional renormalization…
We apply real-space RG methods to study two quantum group invariant Hamiltonians, that of the XXZ model and the Ising model in a transverse field defined in an open chain with appropiate boundary terms. The quantum group symmetry is…
Holographic RG flows are studied in an Einstein-dilaton theory with a general potential. The superpotential formalism is utilized in order to characterize and classify all solutions that are associated to asymptotically AdS space-times.…
We propose a renormalization group scaling function which is constructed from q-deformed fermionic versions of Virasoro characters. By comparison with alternative methods, which take their starting point in the massive theories, we…
Foundations of the formal series $*$ -- calculus in deformation quantisation are discussed. Several classes of continuous linear functionals over algebras applied in classical and quantum physics are introduced. The notion of nonnegativity…
We use the functional Renormalisation Group (fRG) to describe the in and out of equilibrium dynamics of stochastic processes, governed by an overdamped Langevin equation. Exploiting the connection between Langevin dynamics and…
This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmermann 70th birthday. The historical overview (Part 1) partially overlaps with corresponding text of my previous commemorative paper. At the same time…
We derive an expansion of the functional renormalization (fRG) equations that treats the frequency and momentum dependencies of the vertices in a systematic manner. The scheme extends the channel-decomposed fRG equations to the frequency…
The summation of logarithmic contributions to perturbative radiative corrections in physical processes through use of the renormalization group equation has proved to be a useful way of enhancing the information one can obtain from explicit…