Related papers: Convergence from Divergence
We present a nonrelativistic one-particle quantum mechanics whose perturbative S-matrix exhibits a renormalon divergence that we explicitely compute. The potential of our model is the sum of the 2d Dirac $\delta$-potential -- known to…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
We give a transform of convergent trigonometric series into equivalent convergent series and sufficient conditions for the transformed series to converge faster than the original one.
We consider meromorphic transforms given by meromorphic kernels and study their asymptotic expansions under a certain rescaling. Under decay assumptions we establish the full asymptotic expansion in the rescaling parameter of these…
We study a natural nonlinear analogue of Fourier series. Iterative Blaschke factorization allows one to formally write any holomorphic function $F$ as a series which successively unravels or unwinds the oscillation of the function $$ F =…
We investigate the divergent perturbative series of correlation functions for a massless, self-interacting scalar field in de Sitter space. First, we use our previously proposed method of autonomous equations to obtain finite time-dependent…
We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
We consider the Dirichlet problem for equation involving a general operator associated with a symmetric transient regular Dirichlet form and bounded Borel measure on the right-hand side of the equation. We introduce a new function space…
Shrinkage of large particles, either through depolymerisation (i.e. progressive shortening) or through fragmentation (breakage into smaller pieces) may be modelled by discrete equations, of Becker-D\''oring type, or by continuous ones. In…
We propose a new approach to temporal inference, inspired by the Pearlian causal inference paradigm - though quite different from Pearl's approach formally. Rather than using directed acyclic graphs, we make use of factored sets, which are…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
We give an explicit demonstration that the derivative expansion of the QED effective action is a divergent but Borel summable asymptotic series, for a particular inhomogeneous background magnetic field. A duality transformation B\to iE…
Slowly convergent series and sequences as well as divergent series occur quite frequently in the mathematical treatment of scientific problems. In this report, a large number of mainly nonlinear sequence transformations for the acceleration…
The stationary Maxwell-Born-Infeld field equations of electromagnetism with integrable regular sources in a Hoelder space are solved using a perturbation series expansion in powers of Born's electromagnetic constant. The convergence of the…
We present a method for evaluating divergent non-Borel-summable series by an analytic continuation of variational perturbation theory. We demonstrate the power of the method by an application to the exactly known partition function of the…
The theory of scale relativity provides a new insight into the origin of fundamental laws in physics. Its application to microphysics allows us to recover quantum mechanics as mechanics on a non-differentiable (fractal) spacetime. The…
Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to…
We elaborate on the resurgence analysis on the $T\overline{T}$-deformed 2d conformal field theory (CFT). Writing the deformed partition function as an infinite series in the deformation parameter $\lambda$, we develop efficient analytical…
Power series expansions naturally arise whenever solutions of ordinary differential equations are studied in the regime of perturbation theory. In the case of quasi-periodic solutions the issue of convergence of the series is plagued of the…