Related papers: Convergence from Divergence

The Relativistic Dynamical Inversion technique, a novel tool for finding analytical solutions to the Dirac equation, is written in explicitly covariant form. It is then shown how the technique can be used to make a change from Cartesian to…

The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in…

The resummation of superfactorially divergent series represents a significant computational challenge in mathematical physics. In the present paper the resummation of a specific class of Stieltjes series characterized by a moment sequence…

For a power series which converges in some neighborhood of the origin in the complex plane, it turns out that the zeros of its partial sums---its sections---often behave in a controlled manner, producing intricate patterns as they converge…

In this article we study the Dyson Bessel process, which describes the evolution of singular values of rectangular matrix Brownian motions, and prove a large deviation principle for its empirical particle density. We then use it to obtain…

By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…

Using a regularization by putting the system in finite volume, we develop a novel approach to form factor perturbation theory for nonintegrable models described as perturbations of integrable ones. This permits to go beyond first order in…

We recently derived the Hamiltonian of fermionic composites by an exact procedure of bosonization. In the present paper expand this Hamiltonian in the inverse of the number of fermionic states in the composite wave function and give the…

Building on previous work [N. Read, Phys. Rev. B 58, Z. Dong and T. Senthil, 16262 (1998); Phys. Rev. B 102, 205126 (2020)] on the system of bosons at filling factor $\nu = 1$, we derive the Dirac composite fermion theory for a half-filled…

The main issue of this work consists in extracting one or several finite values for the sum of series involved in perturbation theories. It is supposed to work for all cases in which two physical parameters are involved, and makes thorough…

It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and…

Complex dynamical systems are prevalent in many scientific disciplines. In the analysis of such systems two aspects are of particular interest: 1) the temporal patterns along which they evolve and 2) the underlying causal mechanisms.…

In this paper, we consider a q-analogue of the Borel-Laplace summation where q>1 is a real parameter. In particular, we show that the Borel-Laplace summation of a divergent power series solution of a linear differential equation can be…

We study weak convergence of a sequence of point processes to a scale-invariant simple point process. For a deterministic sequence $(z_n)_{n\in\mathbb{N}}$ of positive real numbers increasing to infinity as $n \to \infty$ and a sequence…

Sector decomposition is a constructive method to isolate divergences from parameter integrals occurring in perturbative quantum field theory. We explain the general algorithm in detail and review its application to multi-loop Feynman…

Martingale methods are used to study the almost everywhere convergence of general function series. Applications are given to ergodic series, which improves recent results of Fan \cite{FanETDS}, and to dilated series, including Davenport…

Fractonic matter with dipole symmetry can be coupled to a two-index symmetric tensor gauge field. In this work, we show that this symmetric tensor field, along with other related generalized Maxwell theories, can be consistently coupled to…

Analytical solutions to nonlinear differential equations -- where they exist at all -- can often be very difficult to find. For example, Duffing's equation for a system with cubic stiffness requires the use of elliptic functions in the…

We introduce a systematic approach for the resummation of perturbative series which involve large logarithms not only due to large invariant mass ratios but large rapidities as well. Series of this form can appear in a variety of gauge…

We compare the structures and methods in the theory of causal fermion systems with approaches to fundamental physics based on division algebras, in particular the octonions. We find that octonions and, more generally, tensor products of…