Related papers: Regularization of Diagrammatic Series with Zero Co…
In rigidly supersymmetric quantum theories, the Nicolai map allows one to turn on a coupling constant (from zero to a finite value) by keeping the (free) functional integration measure but subjecting the fields to a particular nonlocal and…
In this paper, by making use of the perturbative expansion around topological field theory we are trying to understand why the standard perturbation theory for General Relativity, which starts with linearized gravity does not see…
We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a tensor train parsimonious representation of the sum of all…
The convergence theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is established. Our results complement the divergence theory developed in `Diophantine approximation on planar curves and the…
An overview is given of the methods for treating complicated problems without small parameters, when the standard perturbation theory based on the existence of small parameters becomes useless. Such complicated problems are typical of…
Dyson's model is a one-dimensional system of Brownian motions with long-range repulsive forces acting between any pair of particles with strength proportional to the inverse of distances with proportionality constant $\beta/2$. We give…
Using statistical physics methods, we study generative diffusion models in the regime where the dimension of space and the number of data are large, and the score function has been trained optimally. Our analysis reveals three distinct…
The first work of Dyson relating to random matrix theory, "The dynamics of a disordered linear chain", is reviewed. Contained in this work is an exact solution of a so-called Type I chain in the case of the disorder variables being given by…
The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The…
The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…
We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and…
We present two Fermi-Bose models with an approximate supersymmetry and which can be solved with great accuracy using the renormalization group method. The bosonic parts of these models consist in Dyson's hierarchical model with one and two…
The evolution of a large class of biological, physical and engineering systems can be studied through both dynamical systems theory and Hamiltonian mechanics. The former theory, in particular its specialization to study systems with…
We provide analytical arguments showing that the non-perturbative approximation scheme to Wilson's renormalisation group known as the derivative expansion has a finite radius of convergence. We also provide guidelines for choosing the…
Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with…
We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts…
We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for…
A $q$--deformed anharmonic oscillator is defined within the framework of $q$--deformed quantum mechanics. It is shown that the Rayleigh--Schr\"odinger perturbation series for the bounded spectrum converges to exact eigenstates and…
Projection theorems of divergences enable us to find reverse projection of a divergence on a specific statistical model as a forward projection of the divergence on a different but rather "simpler" statistical model, which, in turn, results…
A new formulation of perturbation theory for a description of the Dirac and scalar fields (the Yukawa model) is suggested. As the main approximation the self-consistent field model is chosen, which allows in a certain degree to account for…