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In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if…
We review some recent results on asymptotic properties of polynomials of large degree, of general holomorphic sections of high powers of positive line bundles over Kahler manifolds, and of Laplace eigenfunctions of large eigenvalue on…
The absence of the quadratic divergence in the Higgs sector of the Standard Model in the dimensional regularization is usually regarded to be an exceptional property of a specific regularization. To understand what is going on in the…
We project the Wilson/Polchinski renormalization group equation onto its uniform external field dependent effective free energy and connected Green's functions. The result is a hierarchy of equations which admits a choice of "natural"…
The replicated field theory of the random field Ising model involves the couplings of replicas of different indices. The resulting correlation functions involve a superposition of different types of long distance behaviours. However the…
Asymptotically exact results are obtained for the average Green function and density of states of a disordered system for a renormalizable class of models (as opposed to the lattice models examined previously [Zh. Eksp. Teor. Fiz. 106…
Consequences of a symmetry, e.g.\ relations amongst Green functions, are renormalization scheme independently expressed in terms of a rigid Ward identity. The corresponding local version yields information on the respective current. In the…
We study exact renormalization group equations in the framework of the effective average action. We present analytical approximate solutions for the scale dependence of the potential in a variety of models. These solutions display a rich…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…
This paper aims at giving a novel approach to investigate the behavior of the renormalization group flow for tensorial group field theories to all orders of the perturbation theory. From an appropriate choice of the kinetic kernel, we build…
We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The…
We study exact renormalization group equations in the framework of the effective average action. We present analytical solutions for the scale dependence of the potential in a variety of models. These solutions display a rich spectrum of…
A general discussion of the renormalization of the quantum theory of a scalar field as an effective field theory is presented. The renormalization group equations in a mass-independent renormalization scheme allow us to identify the…
A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential…
We derive asymptotic freedom and the $SU(3)$ Yang-Mills $\beta$-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size $s$ is introduced. Effective particles…
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…
Energy-dependent Green's functions for the two and three dimensional $\delta$-function plus harmonic oscillator potential systems are derived by incorporating the renormalization and the self-adjoint extension into the Green's function…
This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral…
It is shown that the $n$-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not…
The meaning of local observables is poorly understood in gauge theories, not to speak of quantum gravity. As a step towards a better understanding we study asymptotic (infrared) transformation in local quantum physics. Our observables are…