Related papers: Renormalons and Analytic Properties of the \beta f…
For various two dimensional non linear $\sigma$ models, we present a direct comparison between the $\beta$ functions computed with the $2+\epsilon$ renormalization group and the $\beta$ functions measured by Monte Carlo simulations. The…
The semi-analytical $O(\alpha_s^4)$ expression for the renormalization group $\beta$-function in the ${\rm{V}}$-scheme is obtained in the case of the $SU(N_c)$ gauge group. In the process of calculations we use the existing information…
In usual dimensional counting, momentum has dimension one. But a function f(x), when differentiated n times, does not always behave like one with its power smaller by n. This inevitable uncertainty may be essential in general theory of…
We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta…
Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G. We show that there exist $\alpha_{1},\alpha_{2}\in\mathbb{R}, \beta\in\frac{1}{2}\mathbb{Z}$, and $l\in\mathbb{N}$ such that…
We map the Schwinger--Dyson equation and the renormalization group equation for the massless Wess--Zumino model in the Borel plane, where the product of functions get mapped to a convolution product. The two-point function can be expressed…
The ambiguities inherent in renormalization are considered when using mass-independent renormalization in massless theories that involve two coupling coupling constants. We review how there is no renormalization scheme in which the…
We consider the general supersymmetric one-dimensional quantum system with boundary, critical in the bulk but not at the boundary. The renormalization group flow on the space of boundary conditions is generated by the boundary beta…
We investigate the high-order behavior of perturbative matching conditions in effective field theories. These series are typically badly divergent, and are not Borel summable due to infrared and ultraviolet renormalons which introduce…
We compute the renormalon ambiguity of the static potential, in the limit of a large number of flavors. An extrapolation of the QED result to QCD implies that the large distance behavior of the quark potential is arbitrary in perturbation…
In this paper we introduce some new methods to understand the analytic behaviour of the zeta function of a group. We can then combine this knowledge with suitable Tauberian theorems to deduce results about the growth of subgroups in a…
In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we…
The problem of obtaining a gauge independent beta function for Newton's constant is addressed. By a specific parameterisation of metric fluctuations a gauge independent functional integral is constructed for the semiclassical theory around…
We prove that a singular part $\mu_s$ of a measure $\mu$ satisfying ${\cal A}\mu =0$ for a linear partial differential operator ${\cal A}$ defined on $R^d$ has the range in the intersection of kernels of the principal symbol of ${\cal A}$…
This is a lecture note on the renormalization group theory for field theory models based on the dimensional regularization method. We discuss the renormalization group approach to fundamental field theoretic models in low dimensions. We…
A new technique named Generalized Borel Transform (GBT) is applied to the generating functional of the $\Phi^{4}$ theory in zero dimensions with degenerate minima. The analytical solution of this function, obtained in the non perturbative…
The $\beta$-functions describe how couplings run under the renormalization group flow in field theories. In general, all couplings that respect the symmetry and locality are generated under the renormalization group flow, and the exact…
Consider a class of functions of one real variable with the following uniqueness property: if a function f(x) from the class vanishes on a set of positive measure, then f is the zero function. In many instances, we would like to have a…
For $\alpha$ a positive irrational, let $\mathcal{A}_{\alpha}$ be the subalgebra of continuous functions on the two-torus whose Fourier transform vanishes at $(m, n)$ if $m + \alpha n < 0.$ These algebras were studied by Wermer and others,…
Effective quantum field theories that allow for the possibility of Lorentz symmetry violation can sometimes also include redundancies of description in their Lagrangians. Explicit calculations in a Lorentz-violating generalization of Yukawa…