Related papers: The Relationship between Bare and Renormalized Cou…
Approximate knowledge of the renormalon structure of the Bjorken polarised sum rule (BSR) ${\overline \Gamma}_1^{{\rm p-n}}(Q^2)$ leads to the corresponding BSR characteristic function that allows us to evaluate the leading-twist part of…
We obtain the $\beta$-functions for the two dimensionless couplings of a 4d renormalizable scalar field theory with cubic and quartic 4-derivative interactions. Both couplings can be asymptotically free in the UV, and in some cases also in…
As an alternative to directly integrating their defining equations to find the running coupling $a(\mu)$ and the running mass $m(\mu)$, we expand these quantities in powers of $\ln\left(\frac{\mu}{\mu^\prime}\right)$ and their boundary…
We briefly review how it is possible to derive some exact expressions for the renormalization constants for the MS-like renormalization prescriptions using the arguments based on the renormalization group. These expressions are obtained for…
It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$…
We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the…
We report thermodynamic values of four-point renormalized coupling constant calculated by Monte Carlo simulations in the continuum limits of the lattice versions of the two-dimensional O(2) and O(3) non-linear sigma models. In each case the…
The relation between the pole quark mass and the $\overline{MS}$-renormalized mass is governed by an infrared renormalon singularity, which leads to an ambiguity of order $\Lambda_{QCD}$ in the definition of the pole mass. We use the…
We study a self-interacting scalar field theory in the presence of a \delta-function background potential. The role of surface interactions in obtaining a renormalizable theory is stressed and demonstrated by a two-loop calculation. The…
We study the issue of coupling among 4-simplices in the context of spin foam models obtained from a group field theory formalism. We construct a generalisation of the Barrett-Crane model in which an additional coupling between the normals…
We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a…
The renormalisation group equation for $N$-point correlation functions can be interpreted in a geometrical manner as an equation for Lie transport of amplitudes in the space of couplings. The vector field generating the diffeomorphism has…
We study the renormalization group flow of $\mathbb{Z}_2$-invariant supersymmetric and non-supersymmetric scalar models in the local potential approximation using functional renormalization group methods. We focus our attention to the fixed…
Renormalization ideas can profitably be exploited in conjunction with the superposition principle of boundary conditions in the description of model independent and universal scaling features of the singular and long range Van der Waals…
We consider the extension of the Standard electroweak Model through an $SU(2)$ quadruplet of scalars with hypercharge either $3/2$ or $1/2$ (with an additional reflection symmetry in the latter case). We establish, through $\textit{exact…
We study the most general renormalizable couplings containing Higgs $H(10)$, $D(120)$, $\overline{\Delta}(\overline{126})+ \Delta(126)$, $A(45)$, $E(54)$ and $\Phi(210)$ in the supersymmetric SO(10) models. The Clebsch-Gordan Coefficients…
Methods described in the literature for the computation of the QCD running coupling are essentially all defined with respect to the renormalization group equations and these equations are associated with the method of renormalization for…
We study classically unstable string type configurations and compute the renormalized vacuum polarization energies that arise from fermion fluctuations in a 2+1 dimensional analog of the standard model. We then search for a minimum of the…
Phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method. A general formula for phase diffusion coefficients is…
We study three well known models of matter coupled to the ultraviolet cutoff, quantized radiation field and to the Coulomb potential of arbitrarily many nuclei. Two are nonrelativistic: the first uses the kinetic energy (p+eA(x))^2 and the…