Related papers: Scaling algebras and pointlike fields: A nonpertur…
We study the renormalization of some dimension-4, 7 and 10 operators in a class of nonlinear scalar-tensor theories. These theories are invariant under: (a) linear diffeomorphisms which represent an exact symmetry of the full non-linear…
After a brief presentation of the exact renormalization group equation, we illustrate how the field theoretical (perturbative) approach to critical phenomena takes place in the more general Wilson (nonperturbative) approach. Notions such as…
Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization-group flow valid at all…
We review our recent results on the renormalization procedure for a free quantum scalar field with modified dispersion relations in curved spacetimes. For dispersion relations containing up to $2s$ powers of the spatial momentum, the…
Arguments are provided which show that extension of renormalizability in quantum field theory is possible. A dressed scheme for the perturbation expansion is proposed. It is proven that in this scheme a nonrenormalizable interaction becomes…
We study unitarity and renormalizability in the Lifshitz scalar field theory, which is characterized by an anisotropic scaling between the space and time directions. Without the Lorentz symmetry, both the unitarity and the renormalizability…
"Preprint" of paper from 1989 that wasn't arxiv'ed at the time. Abstract: Our understanding of quantum field theories, and, in particular, of renomalization has changed radically in recent years; renormalization is no longer a deeply…
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over…
Some form of nonperturbative regularization is necessary if effective field theory treatments of the NN interaction are to yield finite answers. We discuss various regularization schemes used in the literature. Two of these methods involve…
Several issues in the modal approach to quantum field theory are discussed. Within the formalism of spherical field theory, differential renormalization is presented and shown to result in a finite number of renormalization parameters.…
We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…
The 1/N expansion in quantum field theory is formulated within an algebraic framework. For a scalar field taking values in the $N$ by $N$ hermitian matrices, we rigorously construct the gauge invariant interacting quantum field operators in…
These are introductory lecture notes aimed at beginning graduate students covering fundamental concepts and ideas behind the renormalisation group. Our main goal is to motivate it and then explore its consequences, in the context of quantum…
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under…
A formal expansion for the Green's functions of an interacting quantum field theory in a parameter that somehow encodes its "distance" from the corresponding non-interacting one was introduced more than thirty years ago, and has been…
Concerning renormalisation group theory applied to phase transitions, we examine the value of positive numerical and analytical evidence, the divergent short-wavelength behaviour of classical free fields and the absence of UV-divergences in…
The renormalization method is specifically aimed at connecting theories describing physical processes at different length scales and thereby connecting different theories in the physical sciences. The renormalization method used today is…
We review some aspects of non commutative quantum field theory and group field theory, in particular recent progress on the systematic study of the scaling and renormalization properties of group field theory. We thank G. Zoupanos and the…
In close analogy to the Bloch-Feshbach formalism known from the theory of nuclear dynamics, I develop a mathematical framework that allows one to understand renormalization in terms of purely algebraic operations (projections, dilatations)…
Based upon the intrinsic relation between the divergent lower point functions and the convergent higher point ones in the renormalizable quantum field theories, we propose a new method for regularization and renormalization in QFT. As an…