Related papers: Running coupling expansion for the renormalized $\…
The running coupling of a generic field theory can be described through a separable differential equation involving the corresponding $\beta$-function. Only the first loop order can be solved analytically in terms of well-known functions,…
We discuss a D-dimensional Euclidean scalar field interacting with a scale invariant quantized metric. We assume that the metric depends on d-dimensional coordinates where d<D. We show that the interacting quantum fields have more regular…
We discuss a resummed perturbation theory based on the Wilson renormalization group. In this formulation the Wilsonian flowing couplings, which generalize the running coupling, enter directly into the loop expansion. In the case of an…
In this paper we establish an exact relationship between the asymptotic probability distributions $\nu_0$ and $\nu_2$ of the multiple point range of the planar random walk and the proper functions $\Gamma^{[0]}$ and $\Gamma^{[2]}$…
We show that the direction of renormalization in effective field theory is constrained by fundamental principles in the infrared$\unicode{x2014}$unitarity, analyticity, and Lorentz invariance. Our theorem, in the spirit of the $a$-theorem…
For a large class of field theories there exist portions of parameter space for which the loop expansion predicts increased symmetry breaking at high temperature. Even though this behavior would clearly have far reaching implications for…
The analytical method of QCD running coupling constant is extended to a model with an all-order beta function which is inspired by the famous Novikov-Shifman-Vai\-n\-s\-htein-Zakharov beta function of N=1 supersymmetric gau\-g\-e theories.…
We discuss the calculation of the 1-loop effective action on four dimensional, canonically deformed Euclidean space. The theory under consideration is a scalar $\phi^4$ model with an additional oscillator potential. This model is known to…
The basis of the $\{\beta\}$-expansion for the perturbative series evaluated in the $\overline{MS}$ scheme for the renormalization group invariant quantities is summarized.Comparison with a similar representation,used within the…
We develop an efficient algorithm for evaluating divergent perturbation expansions of field theories in the bare coupling constant g_B for which we possess a finite number L of expansion coefficients plus two more informations: The…
The structure of the QFT expansion is studied in the framework of a new "Invariant analytic" version of the perturbative QCD. Here, an invariant (running) coupling $a(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi$ is transformed into a…
I give an overview over some work on rigorous renormalization theory based on the differential flow equations of the Wilson-Wegner renormalization group. I first consider massive Euclidean $\phi_4^4$-theory. The renormalization proofs are…
We present a new approach to calculation of anomalous dimensions in the framework of $\epsilon$-expansion and renormalization group method. This approach allows one to skip the calculation of renormalization constants and express anomalous…
In the recent years, field theory on non-commutative (NC) spaces has attracted a lot of attention. Most literature on this subject deals with perturbation theory, although the latter runs into grave problems beyond one loop. Here we present…
Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in…
In this work, we use a specific parameterization of the hypergeometric approximants ( the one by Mera et.al in Phys. Rev. Let. 115, 143001 (2015)) to approximate the seven-loop critical exponent $\nu$ for the $O(2)$-symmetric $\phi^4$…
We present the perturbative renormalization group functions of $O(n)$-symmetric $\phi^4$ theory in $4-2\varepsilon$ dimensions to the sixth loop order in the minimal subtraction scheme. In addition, we estimate diagrams without…
We generalize the notion of an asymptotic weak coupling expansion about an exactly solvable model in quantum mechanics and quantum field theory to an all positive value coupling convergent expansion. This is done by rescaling the variables…
In 3+1 space-time dimensions, fourth order derivative gravity is perturbatively renormalizable. Here it is shown that it describes a unitary theory of gravitons (with/without an additional scalar) in a limited coupling parameter space which…
We discuss the $\{ \beta \}$-expansion for renormalization group invariant quantities tracing this expansion to the different contractions of the corresponding incomplete BPHZ $R$-operation. All of the coupling renormalizations, which…