Related papers: Taming Nonrenormalizability
The free Schroedinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in…
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts…
An interacting scalar field theory in de Sitter space is non-renormalizable for a generic alpha-vacuum state. This pathology arises since the usual propagator used allows for a constructive interference among propagators in loop…
Some considerations showing that renormalizable theories with consistent perturbative theries can not be nonperturbatively finite (in terms of bare parameters) are provided. Accordingly any fundamental unified theory has to be either non…
A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the hamiltonian…
We obtain an explicit expression for the multipoint energy correlations of a non solvable two-dimensional Ising models with nearest neighbor ferromagnetic interactions plus a weak finite range interaction of strength $\lambda$, in a scaling…
There are reasons to believe that the Standard Model is only an effective theory, with new Physics lying beyond it. Supersymmetric extensions are one possibility: they address some of the Standard Model's shortcomings, such as the…
We study the exact renormalization group of the four dimensional phi4 theory perturbatively. We reformulate the differential renormalization group equations as integral equations that define the continuum limit of the theory directly with…
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field.…
It is shown that global fermionic charges induced in vacuum by slowly varying, topologically non-trivial background scalar fields are not renormalized provided that expansion in momenta of background fields is valid. This suggests that…
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,…
An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.
The physical and mathematical mechanism behind diamagnetism of N (finite) spinless bosons (relativistic or non-relativistic) is well known. The mathematical signature of this diamagnetism follows from Kato's inequality while its physical…
We consider the role that gauge symmetry breaking terms play on the continuum limit of gauge theories in three dimensions. As a paradigmatic example we consider scalar electrodynamics in which $N_f$ complex scalar fields interact with a…
We start a systematic analysis of supersymmetric field theories in six dimensions. We find necessary conditions for the existence of non-trivial interacting fixed points. String theory provides us with examples of such theories. We…
Chiral Effective Field Theory ($\chi$EFT) has been extensively used to study the $NN$ interaction during the last three decades. In Effective Field Theories (EFTs) the renormalization is performed order by order including the necessary…
The renormalized zero-momentum four-point coupling $g_r$ of O(N)-invariant scalar field theories in $d$ dimensions is studied by applying the 1/N expansion and strong coupling analysis. The O(1/N) correction to the $\beta$-function and to…
We consider a neutral self-interacting massive scalar field defined in a d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the one-loop perturbative renormalization of this theory in the presence of rigid boundary…
We use functional renormalization group methods to study gravity minimally coupled to a free scalar field. This setup provides the prototype of a gravitational theory which is perturbatively non-renormalizable at one-loop level, but may…
Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been…