Related papers: Topological Regularization
We propose a novel regularization scheme in quantum field theory, denominator regularization (den reg). As simple to apply as dimensional regularization, and similarly compatible with a minimal subtraction renormalization scheme, den reg…
We introduce the method of topological quantization for gravitational fields in a systematic manner. First we show that any vacuum solution of Einstein's equations can be represented in a principal fiber bundle with a connection that takes…
In the framework of dimensional regularization, we propose a generalization of the renormalization group equations in the case of the perturbative quantum gravity that involves renormalization of the metric and of the higher order Riemann…
The paper discusses extensions of the renormalization group (RG) formalism for 3D incompressible Euler equations, which can be used for describing singularities developing in finite (blowup) or infinite time from smooth initial conditions…
Regularity theorems are presented for cosmology and gravitational collapse in non-Riemannian gravitational theories. These theorems establish conditions necessary to allow the existence of timelike and null path complete spacetimes for…
Recently \cite{Horowitz:2022rpp,Horowitz:2022uak}, denominator regularisation (Den. Reg.) scheme has been proposed to handle divergences in quantum field theory. It is shown to yield results as simple as in dimensional regularisation scheme…
A geometric quantization using the topological recursion is established for the compactified cotangent bundle of a smooth projective curve of an arbitrary genus. In this quantization, the Hitchin spectral curve of a rank $2$ meromorphic…
A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a…
We analyze renormalization group (RG) flows in two-dimensional quantum field theories in the presence of redundant directions. We use the operator picture in which redundant operators are total derivatives. Our analysis has three levels of…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
Recent work suggests that topological features of certain quantum gravity theories can be interpreted as particles, matching the known fermions and bosons of the first generation in the Standard Model. This is achieved by identifying…
The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…
For a topological space $X$ we study continuous maps $f : X\to \mathbb R^m$ such that images of every pairwise distinct $k$ points are affinely (linearly) independent. Such maps are called affinely (linearly) $k$-regular embeddings. We…
This paper presents an algebraic formulation of the renormalization group flow in quantum mechanics on flat target spaces. For any interacting quantum mechanical theory, the fixed point of this flow is a theory of classical probability, not…
We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is ``top-down", in the sense that we postulate the form of the…
We analyze critically the renormalization of quantum fields in cosmological spacetimes, using non covariant ultraviolet cutoffs. We compute explicitly the counterterms necessary to renormalize the semiclassical Einstein equations, using…
Topology provides an essential concept for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing realistic applications is that the level of protection displayed in real systems is…
Regular and spherically symmetric black holes that solve the singularity problems of the Schwarzschild solution are phenomenologically viable at large distance but usually suffer from the Cauchy horizon instability. To overcome this…
The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…