Related papers: Gell-Mann--Low scheme for the Standard Model
I define a naturalness criterion formalizing the intuitive notion of naturalness discussed in the literature. After that, using $\phi^4$ as an example, I demonstrate that a theory may be natural in the $MS$-scheme and, at the same time,…
The recently established generalized Gell-Mann--Low theorem is applied in lowest perturbative order to bound-state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann--Low Theorem…
Gell-Mann-Low functions can be calculated by means of perturbation theory and expressed as truncated series in powers of asymptotically small coupling parameters. However, it is necessary to know there behavior at finite values of the…
The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…
Starting from the Lehmann-Symanzik-Zimmermann reduction theorem, we provide a general procedure to extract S-matrix elements from Green functions in arbitrary renormalization schemes.
We introduce a new definition of a model for a formal mathematical system. The definition is based upon the substitution in the formal systems, which allows a purely algebraic approach to model theory. This is very suitable for applications…
We propose a procedure for estimating the parameters of the Mittag-Leffler (ML) and the generalized Mittag-Leffler (GML) distributions. The algorithm is less restrictive, computationally simple, and necessary to make these models usable in…
We provide a Mahler/Elkies-style lower bound for the average values of dynamical Green's functions on the projective line over an arbitrary valued field, and give some dynamical and arithmetic applications.
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
A connection between the General Linear Model (GLM) in combination with classical statistical inference and the machine learning (MLE)-based inference is described in this paper. Firstly, the estimation of the GLM parameters is expressed as…
We derive bounds $ |\frac{d\psi(\alpha)}{d\alpha}| \leq 1 $, $ \frac{d(\frac{d\psi(\alpha)}{d\alpha}\psi(\alpha))}{d\alpha} \leq 1 $ on the GL (Gell-Mann--Low) function $\psi(\alpha)$ from the Kallen-Lehmann dispersion representation in…
In this paper, the Green's function and decomposition technique is proposed for solving the coupled Lane-Emden equations. This approach depends on constructing Green's function before establishing the recursive scheme for the series…
An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the \Phi^4 theory, the algorithm yields the…
Application of the background-field method yields a gauge-invariant effective action for the electroweak Standard Model, from which simple QED-like Ward identities are derived. As a consequence of these Ward identities, the background-field…
This paper presents a brief introduction to the key points of the Grey Machine Learning (GML) based on the kernels. The general formulation of the grey system models have been firstly summarized, and then the nonlinear extension of the grey…
Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…
These lectures aim to provide a basic introduction to dispersive methods and their modern applications to the phenomenology of the Standard Model at low energy. This approach exploits analyticity properties of Green functions and scattering…
Deriving a comprehensive set of reduction rules for Feynman integrals has been a longstanding challenge. In this paper, we present a proposed solution to this problem utilizing generating functions of Feynman integrals. By establishing and…
Representing spectral densities, real-frequency, and real-time Green's functions of continuous systems by a small discrete set of complex poles is an ubiquitous problem in condensed matter physics, with applications ranging from quantum…
In formal scattering theory, Green functions are obtained as solutions of a distributional equation. In this paper, we use the Sturm-Liouville theory to compute Green functions within a rigorous mathematical theory. We shall show that both…