Related papers: Functional self-similarity and renormalization gro…
It is shown that the renormalization group turns to be a symmetry group in a theory initially formulated in a space of scale-dependent functions, i.e, those depending on both the position $x$ and the resolution $a$. Such theory, earlier…
A novel method of summation for power series is developed. The method is based on the self-similar approximation theory. The trick employed is in transforming, first, a series expansion into a product expansion and in applying the…
Real Space Renormalization Group (RSRG) techniques and their applications, mainly to quantum mechanics and to partial differential equations, are discussed. Special emphasis is given to the theoretical insight and the reasons for the…
Starting from a representation of the early time evolution of a dynamical system in terms of the polynomial expression of some observable f (t) as a function of the time variable in some interval 0 < t < T, we investigate how to…
The study of nonlinear phenomena in systems with many degrees of freedom often relies on complex numerical simulations. In trying to model realistic situations, these systems may be coupled to an external environment which drives their…
A method is described to probe high-scale physics in lower-energy experiments by employing sum rules in terms of renormalisation group invariants. The method is worked out in detail for the study of supersymmetry-breaking mechanisms in the…
Renormalization group methods generate low-resolution Hamiltonians that are more diagonal and easier to solve. This chapter reviews the similarity renormalization group for nuclear Hamiltonians, which is a popular method for generating…
Self-consistent new renormalization group flow equations for an O(N)-symmetric scalar theory are approximated in next-to-leading order of the derivative expansion. The Wilson-Fisher fixed point in three dimensions is analyzed in detail and…
In these notes the exact renormalization group formulation of the scalar theory is briefly reviewed. This regularization scheme is then applied to supersymmetric theories. In case of a supersymmetric gauge theory it is also shown how to…
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…
General issues concerning the regularization of supersymmetric theories using dimensional regularization and dimensional reduction are reviewed. Recent progress on problems of dimensional reduction related to factorization, supersymmetry,…
Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops. The resulting flow equations can…
We study the renormalization group equations of the fully anisotropic $\lambda$-deformed CFTs involving the direct product of two current algebras at different levels $k_{1,2}$ for general semi-simple groups. The exact, in the deformation…
The renormalization group method is a successive integration over the fluctuations which are ordered according to their length scale, a parameter in the external space. A different procedure is described, where the fluctuations are treated…
We develop a unified categorical framework for gauging both continuous and finite symmetries in arbitrary spacetime dimensions. Our construction applies to geometric categories i.e. categories internal to stacks. This generalizes the…
First-order `Bogomol'nyi' equations are found for dilaton domain walls of D-dimensional gravity with the general dilaton potential admitting a stable anti-de Sitter vacuum. Implications for renormalization group flow in the holographically…
Real-Space renormalization group techniques are developed for tackling large curvature fluctuations in quantum gravity. Within cells of invariant volume $a^4$, only certain types of fluctuations are allowed. Normal coordinates are used to…
We consider the method of self-similar renormalization for calculating critical temperatures and critical indices. A new optimized variant of the method for an effective summation of asymptotic series is suggested and illustrated by several…
Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…
New estimates of the critical exponents have been obtained from the field-theoretical renormalization group using a new method for summing divergent series. The results almost coincide with the central values obtained by Le Guillou and…