Related papers: Resummation and renormalons in a general Quantum F…
The idea of reduction of couplings in renormalizable theories will be presented and then will be applied in Particle Physics models. Reduced couplings appeared as functions of a primary one, compatible with the renormalization group…
The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of…
In this paper we construct the 2 dimensional Euclidean $\phi^4$ quantum field theory using the method of loop vertex expansion. We reproduce the results of standard constructive theory, for example the Borel summability of the Schwinger…
Some quantum mechanical potentials, singular at short distances, lead to ultraviolet divergences when used in perturbation theory. Exactly as in quantum field theories, but much simpler, regularization and renormalization lead to finite…
A class of exact infinitesimal renormalization group transformations is proposed and studied. These transformations are pure changes of variables (i.e., no integration or elimination of some degrees of freedom is required) such that a…
That the exact quantum S-matrix of $\text{T}\bar{\text{T}}$-deformed field theories is known has interesting consequences for their perturbative renormalisation. Recent investigations into the interplay between renormalisation and…
We discuss Hamiltonian learning in quantum field theories as a protocol for systematically extracting the operator content and coupling constants of effective field theory Hamiltonians from experimental data. Learning the Hamiltonian for…
In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel…
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…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
The general theory of the reduction in the number of coupling parameters is discussed. The method involves renormalization group invariant relations between couplings. It is more general than the imposition of symmetries. There are reduced…
We present an overview of the phenomenological implications of the theory of resummed quantum gravity. We discuss its prediction for the cosmological constant in the context of the Planck scale cosmology of Bonanno and Reuter, its…
In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces…
We derive several results concerning non-perturbative renormalization in the spherical field formalism. Using a small set of local counterterms, we are able to remove all ultraviolet divergences in a manner such that the renormalized theory…
We analize the impact of two-loop renormalization group equations on the $SU(3)_c\times SU(2)_w\times U(1)_Y$ gauge couplings unification in various supersymmetric theories. In general the presence of superfields in higher representation…
We give an indication that gravity coupled to an infinite number of fields might be a renormalizable theory. A toy model with an infinite number of interacting fermions in four-dimentional space-time is analyzed. The model is finite at any…
We review the techniques used to renormalize quantum field theories at several loop orders. This includes the techniques to systematically extract the infinities in a Feynman integral and the implementation of the algorithm within computer…
In a previous paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187) we presented a new method for renormalization in Euclidean configuration spaces based on certain renormalization maps. This…
We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent…
Very high energy physics needs a coherent description of the four fundamental forces. Non-commutative geometry is a promising mathematical framework which already allowed to unify the general relativity and the standard model, at the…