Related papers: Renormalization in quantum field theory and the Ri…
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
In 1999, A. Connes and D. Kreimer have discovered the Hopf algebra structure on the Feynman graphs of scalar field theory. They have found that the renormalization can be interpreted as a solving of some Riemann -- Hilbert problem. In this…
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…
We provide a self-contained formulation of the BPHZ theorem in the Euclidean context, which yields a systematic procedure to "renormalise" otherwise divergent integrals appearing in generalised convolutions of functions with a singularity…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
The second alternative conformal limit of the recently proposed general higher derivative dilaton quantum theory in curved spacetime is explored. In this version of the theory the dilaton is transformed, along with the metric, to provide…
Approximately 10 years ago, the method of renormalization-group symmetries entered the field of boundary value problems of classical mathematical physics, stemming from the concepts of functional self-similarity and of the Bogoliubov…
The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This…
Conventional renormalization methods in statistical physics and lattice quantum field theory assume a flat metric background. We outline here a generalization of such methods to models on discretized spaces without metric background.…
We derive new expressions for the Rayleigh-Schr\"odinger seriesdescribing the perturbation of eigenvalues of quantumHamiltonians. The method, somehow close to the so-called dimensionalrenormalization in quantum field theory, involves the…
In the practice of physics model building, the process of renormalization, resummation, and anomaly cancellation is to incrementally repair initially ill-defined Lagrangian quantum field theories. Impressive as this is, one would rather…
We explore quantum field theories with fractional d'Alembertian $\Box^\gamma$. Both a scalar field theory with a derivative-dependent potential and gauge theory are super-renormalizable for a fractional power $1<\gamma\leq 2$, one-loop…
A Lagrange multiplier field restricts the quantum corrections to the Einstein-Hilbert action at one-loop order, yielding a model that is renormalizable and unitary while reproducing the Einstein field equations in the classical limit.
The general features of renormalization and the renormalization group in QED and in general quantum field theories in curved spacetime with additional Lorentz- and CPT-violating background fields are reviewed.
The exact one-loop beta functions for the four-derivative terms (Weyl tensor squared, Ricci scalar squared and the Gauss-Bonnet) are derived for the minimal six-derivative quantum gravity (QG) theory in four spacetime dimensions. The…
A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low dimensional theories and of non-polynomial interactions. We discuss the connection between the…
New proves of decoupling of massive fields in several quantum field theories are derived in the effective Lagrangian approach based on Wilson renormalization group. In the most interesting case of gauge theories with spontaneous symmetry…
A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the…
The problem of reduction (wave packet reduction) is reexamined under two simple conditions: Reduction is a last step completing decoherence. It acts in commonplace circumstances and should be therefore compatible with the mathematical frame…
We study the one loop renormalization in the most general metric-dilaton theory with the second derivative terms only. The general theory can be divided into two classes, models of one are equivalent to conformally coupled with gravity…