Related papers: Gell-Mann - Low Function in the Phi^4 Theory
Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…
The Weisfeiler-Leman (WL) algorithms form a family of incomplete approaches to the graph isomorphism problem. They recently found various applications in algorithmic group theory and machine learning. In fact, the algorithms form a…
The formulation of the non-linear sigma model in terms of flat connection allows the construction of a perturbative solution of a local functional equation encoding the underlying gauge symmetry. In this paper we discuss some properties of…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
The convergence properties of the resummed thermal perturbation series for the thermodynamic pressure are investigated by comparison with the exact results obtained in large-N phi^4 theory and possibilities for improvements are discussed.…
Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual…
We discuss a new approach of scalar field theory where the small field contributions are treated perturbatively and the large field configurations (which are responsible for the asymptotic behavior of the perturbative series) are neglected.…
We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent gnome-wide association studies. The asymptotic analysis establishes consistency…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
We consider $\phi^3$ theory in $6-2\epsilon$ with $F_4$ global symmetry. The beta function is calculated up to 3 loops, and a stable unitary IR fixed point is observed. The anomalous dimensions of operators quadratic or cubic in $\phi$ are…
We present a general method for extracting the Gell Mann-Low logarithmic derivative of an effective charge of an observable directly from data as a mean for empirically verifying the universal terms of the QCD $\beta$-function. Our method…
Effective potential for scalar $\lambda\phi^4$ theory is obtained using the exact renormalization group method which includes both the usual one-loop contribution as well as the dominant higher loop effects. Our numerical calculation…
High orders in perturbation theory can be calculated by the Lipatov method. For most field theories, the Lipatov asymptotics has the functional form c a^N \Gamma(N+b) (N is the order of perturbation theory); relative corrections to this…
In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of…
This note contains some asymptotic formulas for the sums of various residue classes of Euler's phi-function.
As the number of loops goes to infinity Feynman $\alpha$-parameters undergo a fixing mechanism which entails a gaussian representation for propagators in scalar field theories. Here, we describe this mechanism in the fullest detail. The…
In this paper we continue investigation of the hypergeometric function ${}_4F_3(1)$ as the function of its seven parameters. We deduce several reduction formulas for this function under additional conditions that one of the top parameters…
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical…
We propose the another, in principe nonperturbative, method of the evaluation of the Wiener functional integral for $\phi^4$ term in the action. All infinite summations in the results are proven to be convergent. We finf the "generalized"…
Gravitational contributions to the running of gauge couplings are calculated by using different regularization schemes. As the $\beta$ function concerns counter-terms of dimension four, only quadratic divergences from the gravitational…