Related papers: Angles, scales and parametric renormalization
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
The main theme of the paper is the detailed discussion of the renormalization of the quantum field theory comprising two interacting scalar fields. The potential of the model is the fourth-order homogeneous polynomial of the fields,…
Dependence on the gauge parameters is an important issue in gauge theories: physical quantities have to be independent. Extending BRS transformations by variation of the gauge parameter into a Grassmann variable one can control gauge…
We describe a set of methods to calculate gauge theory renormalization constants from string theory, all based on a consistent prescription to continue off shell open bosonic string amplitudes. We prove the consistency of our prescription…
By identifying each standard flag with a trivalent Feynman diagram, the corresponding propagators can be read directly from the flag itself. Within the flag representation, the kinematic Jacobi identity (equivalently, the residue theorem on…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter…
Early developments leading to renormalizable non-Abelian gauge theories for the weak, electromagnetic and strong interactions, are discussed from a personal viewpoint. They drastically improved our view of the role of field theory, symmetry…
We discuss perturbative solutions of renormalization group equations, and propose the use of resummation scale techniques in assessing theoretical uncertainties on the extraction of parton distribution functions from data.
We demonstrate that in the mass independent renormalization scheme. the renormalization group equations associated with the unphysical parameters that characterize the renormalization scheme and the mass scale leads to summation that…
We show that to n loop order the divergent content of a Feynman amplitude is spanned by a set of basic (logarithmically divergent) integrals which need not be evaluated. Only the coefficients of the basic divergent integrals are necessary…
Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…
We reconsider the choice of renormalization schemes in a differential-equation approach to aid the discussion of the renormalization of the unstable particles and the CKM matrix in the Standard Model. Certain mass dependent schemes do not…
We give a thoroughful explanation of the general properties of different, general scales, corresponding to different (all possible) mathematical functions f(x), we mention and analyse many examples. These observations and statements might…
We construct here the parametric representation of a translation-invariant renormalizable scalar model on the noncommutative Moyal space of even dimension $D$. This representation of the Feynman amplitudes is based on some integral form of…
We perform the renormalization of different types of Two-Higgs-Doublet Models for the calculation of observables at next-to-leading order. In detail, we suggest four different renormalization schemes based on on-shell renormalization…
In the Yukawa model with two different mass scales the renormalization group equation is used to obtain relations between scattering amplitudes at low energies. Considering fermion-fermion scattering as an example, a basic one-loop…
It is shown how nucleon-nucleon potentials can be defined in N dimensions, using dimensional regularization to continue amplitudes. This provides an easy way to separate out contact ($\delta$-function) terms arising from renormalization. An…
Starting from the complete Mellin representation of Feynman amplitudes for noncommutative vulcanized scalar quantum field theory, introduced in a previous publication, we generalize to this theory the study of asymptotic behaviours under…
We present a procedure of differential renormalization at the one loop level which avoids introducing unnecessary renormalization constants and automatically preserves abelian gauge invariance. The amplitudes are expressed in terms of a…