Related papers: Renormalization Group Summation with Heavy Fields
We explicitly compute the critical exponents associated with logarithmic corrections (the so-called hatted exponents) starting from the renormalization group equations and the mean field behavior for a wide class of models at the upper…
The general structure of the renormalization group equations for the low energy effective field theory formulation of pure gravity is presented. The solution of these equations takes a particular simple form if the mass scale of the…
Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can…
We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann-Hilbert problem. Given a loop $\gamma(z), | z |=1$ of elements…
We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field…
The hierarchy problem is associated with renormalization and decoupling. We can account for the smallness of the scalar mass against loop corrections and its insensitivity to ultraviolet physics through the decoupling of heavy fields. It is…
This paper argues that the ideas underlying the renormalization group technique used to characterize phase transitions in condensed matter systems could be useful for distinguishing computational complexity classes. The paper presents a…
The technique known as group averaging provides powerful machinery for the study of constrained systems. However, it is likely to be well defined only in a limited set of cases. Here, we investigate the possibility of using a `renormalized'…
In the analysis of large/big data sets, aggregation (replacing values of a variable over a group by a single value) is a standard way of reducing the size (complexity) of the data. Data analysis programs provide different aggregation…
We determine masses of light quarks ($m_u$,$m_d$,$m_s$) using Borel-Laplace sum rules and renormalization group summed perturbation theory (RGSPT) from the divergence of the axial vector current. The RGSPT significantly reduces the scale…
We suggest that at any given order of Feynman diagram calculation all renormalization group (RG)-predictable terms should be resummed to all-orders. This ``complete'' RG-improvement (CORGI) serves to separate the perturbation series into…
We investigate to what extent renormalization can be understood as an algebraic manipulation on concatenated one-loop integrals. We find that the resulting algebra indicates a useful connection to knot theory.
In some cases the state of a quantum system with a large number of subsystems can be approximated efficiently by the density matrix renormalization group, which makes use of redundancies in the description of the state. Here we show that…
In this talk methods for a rigorous control of the renormalization group (RG) flow of field theories are discussed. The RG equations involve the flow of an infinite number of local partition functions. By the method of exact beta-function…
Multiparticle production in (2+1) dimensions is investigated. We show that in a small region around the threshold the perturbation theory becomes unapplicable due to infrared divergencies in a class of Feynman graphs with rescattering in…
We develop an alternative derivation of the renormalized expression for the one-loop soliton quantum mass corrections in (1+1)-dimensional scalar field theories. We regularize implicitly such quantity by subtracting and adding its…
Renormalization Group Equations in integro-differential form describing the evolution of cascades or resumming logarithmic scaling violations have been known in quantum field theory for a long time. These equations have been traditionally…
The existence of fluctuations together with interactions leads to scale-dependence in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of…
Renormalization procedure is generalized to be applicable for non renormalizable theories. It is shown that introduction of an extra expansion parameter allows to get rid of divergences and express physical quantities as series of finite…
The structure of the renormalization group equations for the low energy effective theory of gravity coupled to a scalar field is presented. An approximate solution to these equations with a finite number of independent renormalized…