Related papers: Renormalization of QED with planar binary trees
It is well known that the quasinormal modes (or resonant states) of photonic structures can be associated with the poles of the scattering matrix of the system in the complex-frequency plane. In this work, the inverse problem, i.e., the…
In this letter the algebraic renormalization method, which is independent of any kind of regularization scheme, is presented for the parity-preserving QED_3 coupled to scalar matter in the symmetric regime, where the scalar assumes…
We extend the results we obtained in an earlier work. The cocommutative case of rooted ladder trees is generalized to a full Hopf algebra of (decorated) rooted trees. For Hopf algebra characters with target space of Rota-Baxter type, the…
We construct a Hopf algebra structure on the space of specified Feynman graphs of a quantum field theory. We introduce a convolution product and a semigroup of characters of this Hopf algebra with values in some suitable commutative algebra…
A novel, non-power, expansion of QCD quantities replacing the standard perturbative expansion in powers of the renormalized couplant a has recently been introduced and examined by two of us. Being obtained by analytic continuation in the…
In this letter the algebraic renormalization method, which is independent of any kind of regularization scheme, is presented for the parity-preserving QED_3 coupled to scalar matter in the broken regime, where the scalar assumes a finite…
Computing all divergent one-loop Green's functions of \theta-expanded noncommutative quantum electrodynamics up to first order in \theta, we show that this model is not renormalizable. The reason is a divergence in the electron four-point…
A certain pattern of divergence of perturbative expansions in quantum field theories, related to their small and large momentum behaviour, is known as renormalons. We review formal and phenomenological aspects of renormalon divergence. We…
Perturbative expansions of QCD observables in powers of $\alpha_s$ are believed to be asymptotic and non-Borel summable due to the existence of singularities in the Borel plane (renormalons). This fact is connected with the factorization of…
In this work we present the study of the renormalizability of the Generalized Quantum Electrodynamics ($GQED_{4}$). We begin the article by reviewing the on-shell renormalization scheme applied to $GQED_{4}$. Thereafter, we calculate the…
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 investigate the properties of quantum electrodynamics $(QED_3)$ in two spatial dimensions at finite temperature and density. The static as well as the dynamical properties of the planar plasma are calculated using the real time formalism…
The Hopf algebra of renormalization in quantum field theory is described at a general level. The products of fields at a point are assumed to form a bialgebra B and renormalization endows T(T(B)^+), the double tensor algebra of B, with the…
In this article, we review the principles of macroscopic quantum electrodynamics and discuss a variety of applications of this theory to medium-assisted atom-field coupling and dispersion forces. The theory generalises the standard mode…
The idea of the modal expansion in electromagnetics is derived from the research on electromagnetic resonators, which play an essential role in developments in nanophotonics. All of the electromagnetic resonators share a common property:…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
Perturbation expansions appear to be divergent series in many physically interesting situations, including in quantum field theories like quantum electrodynamics (QED) and quantum chromodynamics (QCD), where the perturbative coefficients…
Using thermal field theory, we derive simple analytic expressions for the spectral density of photons in degenerate QED plasmas, without assuming the usual non or ultra-relativistic limit. We recover the standard results in both cases.…
The problem of two coupled scalar fields, one with mass much lighter than the other is analysed by means of Wilson's renormalization group approach. Coupled equations for the potential and the wave function renormalization are obtained by…
In light of the conference Quantum Mathematical Physics held in Regensburg in 2014, we give our perspective on the external field problem in quantum electrodynamics (QED), i.e., QED without photons in which the sole interaction stems from…