Related papers: Numbers and Functions in Quantum Field Theory
We derive an algorithm for automatic calculation of perturbative $\beta$-functions and anomalous dimensions in any local quantum field theory with canonical kinetic terms. The infrared rearrangement is performed by introducing a common mass…
We consider the problem of determining the beta-functions for any reduced effective field theory. Even though not all the Green's functions of a reduced effective field theory are renormalizable, unlike the full effective field theory,…
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 previous attempts of reconstructing the Gell-Mann-Low function \beta(g) of the \phi^4 theory by summing perturbation series give the asymptotic behavior \beta(g) = \beta_\infty g^\alpha in the limit g\to \infty, where \alpha \approx 1…
We calculate the renormalization constants of the N=1, N=2, N=4 supersymmetric Yang-Mills theories in an arbitrary covariant gauge in the dimensional reduction scheme up to three loops. We have found, that the beta-functions for N=1 and N=4…
The renormalization group method is applied to the three-loop effective potential of the massive $\phi^4$ theory in the $\bar{\rm MS}$ scheme in order to obtain the next-next-next-to-leading logarithm resummation. For this, we exploit…
A new approach to generalised Casimir type of problems is derived within the context of renormalisable quantum field theory (QFT). We study the simplest case of a massive fluctuating boson field coupled to a time-independent background…
In this study, we propose a novel regularization/renormalization scheme that utilizes an auxiliary Feynman parameterization. This approach is employed to align a specified loop diagram with a designated unit of the form $1=\lambda/\lambda$.…
We propose an implicit regularisation scheme. The main advantage is that since no explicit use of a regulator is made, one can in principle avoid undesirable symmetry violations related to its choice. The divergent amplitudes are split into…
The Fermi function $F(Z,E)$ accounts for QED corrections to beta decays that are enhanced at either small electron velocity $\beta$ or large nuclear charge $Z$. For precision applications, the Fermi function must be combined with other…
The renormalization of composite operators is a fundamental aspect of quantum field theory, relevant for the description of phase transitions and high energy phenomenology. We calculate the anomalous dimensions of a large set of operators…
We present a quick introduction to quantum field theory and Wilson's theory of the renormalization group from the point of view of mathematical analysis. The presentation is geared primarily towards a probability theory, harmonic analysis…
We discuss conceptual aspects of renormalization in the context of effective field theories for the two-nucleon system. It is shown that, contrary to widespread belief, renormalization scheme dependence of the scattering amplitude can only…
We present general four-loop template $\beta$-functions and anomalous field dimensions for renormalisable scalar-fermion theories in three dimensions. By imposing $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry, we obtain relations…
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
We demonstrate our simple strategy for renormalization with QED at one-loop level, basing on an elaboration of the effective field theory philosophy. No artificial regularization or deformation of the original theory is introduced here and…
It has been previously shown that calculation of renormalization group (RG) functions of the scalar \phi^4 theory reduces to the analysis of thermodynamic properties of the Ising model. Using high-temperature expansions for the latter, RG…
Starting from a well defined local Lagrangian, we analyze the renormalization group equations in terms of the two different arbitrary scales associated with the regularization procedure and with the physical renormalization of the bare…
A two-loop calculation of the renormalization group $\beta$--function in a momentum subtraction scheme with massive quarks is presented using the background field formalism. The results have been obtained by using a set of new generalized…
We compute the beta functions for the three gauge couplings of the Standard Model in the minimal subtraction scheme to three loops. We take into account contributions from all sectors of the Standard Model. The calculation is performed…