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We show that Minkowski higher-derivative quantum field theories are generically inconsistent, because they generate nonlocal, non-Hermitian ultraviolet divergences, which cannot be removed by means of standard renormalization procedures. By…
In this paper we present a stepwise construction of the path integral over relativistic orbits in Euclidean spacetime. It is shown that the apparent problems of this path integral, like the breakdown of the naive Chapman-Kolmogorov…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We introduce the {\em pair-cut cone $PCUT_n$} of metrics on sets with $n\ge 3$ elements, that correspond to linear combinations with non-negative coefficients of the cut-metrics resulting from cuts that are pairs. Given a metric, we fully…
Technical aspects of the Shirkov-Solovtsov's analytic perturbation theory (APT) are considered. We construct explicitly two sets of specific functions, ${\mathfrak{A}_n(s)}$ and ${{\cal A}_n(Q^2)}$ that determine the nonpower as ymptotic…
Economists often rely on estimates of linear fixed effects models produced by other teams of researchers. Assessing the uncertainty in these estimates can be challenging. I propose a form of sample splitting for networks that partitions the…
In this paper we aim to use different metrics in the Euclidean space and Sobolev type metrics in function spaces in order to produce reliable parameters for the differentiation of point distributions and dynamical systems. The main tool is…
A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…
In this paper we present a novel technique based on deep reinforcement learning that allows for numerical analytic continuation of integrals that are often encountered in one-loop diagrams in quantum field theory. In order to extract…
We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two point correlation and the pair velocity for Gaussian initial conditions in a critical density matter dominated cosmological…
We give a universal formula describing derivation operators on a Hilbert space for a large class of interpolation methods. It is based on a simple new technique on ``critical points" where all the derivations attain the maximum. We deduce…
We study the level sets of the distance function from a boundary point of a convex set in Euclidean space. We provide a lower bound for the range of connectivity of the level sets, in terms of the critical points of the distance function in…
We give a microscopic derivation of time-dependent correlation functions of the $1D$ cubic nonlinear Schr\"{o}dinger equation (NLS) from many-body quantum theory. The starting point of our proof is our previous work on the time-independent…
We consider two-dimensional conformal field theories (CFTs), which exhibit a hallmark feature of quantum chaos: universal repulsion of energy levels as described by a regime of linear growth of the spectral form factor. This physical input…
Lattice quantum chromodynamics (QCD) provides the only known systematic, nonperturbative method for first-principles calculations of nucleon structure. However, for quantities such as lightfront parton distribution functions (PDFs) and…
We introduce methods which allow observed galaxy clustering to be used together with observed luminosity or stellar mass functions to constrain the physics of galaxy formation. We show how the projected two-point correlation function of…
We investigate the 2-point correlation function for the vector current. The gluons provide dressings for both the quark self energy as well as the vector vertex function, which are described consistently by the rainbow Dyson-Schwinger…
Smoluchowski's equation is a macroscopic description of a many particle system with coagulation and shattering interactions. We give a microscopic model of the system from which we derive this equation rigorously. Provided the existence of…
The classification of shapes is of great interest in diverse areas ranging from medical imaging to computer vision and beyond. While many statistical frameworks have been developed for the classification problem, most are strongly tied to…
We propose a method to reconstruct smeared spectral functions from two-point correlation functions measured on the Euclidean lattice. Arbitrary smearing function can be considered as far as it is smooth enough to allow an approximation…