Related papers: Naturalness and Renormalization Group in the Stand…
In the first part of this paper the notion of natural metric on the set of natural numbers is defined. It is such metric that the completion of N is a compact metric space that a probability borel measure exists in order that the sequence…
We consider the gauge invariance of the standard Yang-Mills model in the framework of the causal approach of Epstein-Glaser and Scharf and determine the generic form of the anomalies. The method used is based Epstein-Glaser approach to…
Most complex machine learning and modelling techniques are prone to over-fitting and may subsequently generalise poorly to future data. Artificial neural networks are no different in this regard and, despite having a level of implicit…
Relations between some kinds of formal and standard smoothness, for morphisms of schemes, are clarified in surprisingly simple and direct ways, bypassing much of the customarily employed machinery. Even the deep local-to-global property of…
The renormalization of the Minimal Supersymmetric Standard Model is discussed. In particular we focus on the soft-supersymmetry breaking sector of the MSSM and comment on non-renormalization theorems.
The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a $\mathbb{Z}_3$…
Satisfiability is a classic problem in computational complexity theory, in which one wishes to determine whether an assignment of values to a collection of Boolean variables exists in which all of a collection of clauses composed of logical…
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology - that uses renormalization group theory - for finding out existence of periodic…
A central problem in proof-theory is that of finding criteria for identity of proofs, that is, for when two distinct formal derivations can be taken as denoting the same logical argument. In the literature one finds criteria which are…
Using the machinery of smooth scaling and coarse-graining of observables, developed recently in the context of so-called fluctuation operators (originally developed by Verbeure et al), we extend this approach to a rigorous renormalisation…
The perturbative $\beta$-function is known exactly in a number of supersymmetric theories and in the 't Hooft renormalization scheme in the $\phi_4^4$ model. It is shown how this allows one to compute the effective action exactly for…
We propose a model-independent framework to classify and study neutrino mass models and their phenomenology. The idea is to introduce one particle beyond the Standard Model which couples to leptons and carries lepton number together with an…
The exact renormalisation group equation is studied for a two-dimensional theory with exponential interaction and a background charge at infinity. The motivation for studying this interaction is the flow between unitary minimal models…
Scalar field theory at finite temperature is investigated via an improved renormalization group prescription which provides an effective resummation over all possible non-overlapping higher loop graphs. Explicit analyses for the lambda…
In previous work, I described several examples combining reduction and emergence: where reduction is understood a la Ernest Nagel, and emergence is understood as behaviour or properties that are novel (by some salient standard). Here, my…
In optimal prediction methods one estimates the future behavior of underresolved systems by solving reduced systems of equations for expectations conditioned by partial data; renormalization group methods reduce the number of variables in…
Combining the Kaplan surface mode approach for chiral fermions with added terms motivated by Eichten and Preskill suggests the possibility for a lattice regularization of the standard model which is finite, exactly gauge invariant, and only…
The structure of the MSSM is reviewed. We first motivate the particle content of the theory by examining the quantum numbers of the known standard model particles and by the requirement of anomaly cancellation. Once the particle content is…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
We use a renormalization group method, similar to that developed for random spin chains, to infer information about the layouts of cellular wireless networks.