Related papers: Finiteness following from underlying theory: a nat…
Within the framework of the recently proposed Taylor-Lagrange regularization procedure, we reanalyze the calculation of radiative corrections in $QED$ at next to leading order. Starting from a well defined local bare Lagrangian, the use of…
We show that it is not possible to UV-complete certain low-energy effective theories with spontaneously broken space-time symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken…
A well-known topic within the philosophy of physics is the problem of fine-tuning: the fact that the universal constants seem to take non-arbitrary values in order for live to thrive in our Universe. In this paper we will talk about this…
We reconsider the naturalness from the viewpoint of effective field theories, motivated by the alternative scenario that the standard model holds until a high-energy scale such as the Planck scale. We propose a calculation scheme of…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
An affine quantization approach leads to a genuine quantum theory of general relativity by extracting insights from a short list of increasingly more complex, soluble, perturbably nonrenormalizable models.
We introduce regular charts as physical reference frames in spacetime, and we show that general spacetimes can always be fully captured by regular charts. Effective quantum field theories (QFTs) can be conveniently defined in regular…
In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…
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…
I comment and summarize the principles underlying the Four Dimensional Regularization/Renormalization (FDR) approach to the UV and IR infinities. A few recent results are also reviewed.
Recently, various natural algorithmic problems have been shown to be $\exists \mathbb{R}$-complete. The reduction relied in many cases on the $\exists \mathbb{R}$-completeness of the problem ETR-INV, which served as a useful intermediate…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
Effective Field Theories with higher derivatives often yield equations of motion which define ill-posed problems. We present a method for enhancing control on such theories by coupling them to a field living in one extra dimension. The…
We present infinite extensive strategy profiles with perfect information and we show that replacing finite by infinite changes the notions and the reasoning tools. The presentation uses a formalism recently developed by logicians and…
We consider a finite universe U (more exactly - a family U of them) and second order quantifiers Q_K, where for each U this means quantifying over a family of n(K)-place relations closed under permuting U. We define some natural orders and…
With the present trend in experimental particle physics of probing yet shorter distances and with the requirement on the theoretical side of renormalizability, conformal invariance becomes an attractive symmetry for particle interactions.…
A manifestly gauge invariant exact renormalization group for pure SU(N) Yang-Mills theory is proposed, allowing gauge invariant calculations, without any gauge fixing or ghosts. The necessary gauge invariant regularisation which implements…
Finite Unified Theories (FUTs) are N=1 supersymmetric Grand Unified Theories that can be made all-loop finite, leading to a severe reduction of the free parameters. We review the investigation of FUTs based on SU(5) in the context of…
It is argued that the occurrence of disproportionately ("un-natural") large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is…
We discuss aspects of the hierarchy problem in effective theories with light scalars and a large, physical ultraviolet (UV) cutoff. We make two main points: (1) The (naive) fine-tuning observed in an effective theory does not automatically…