Related papers: Bethe-Salpeter Equation -- The Origins
The report deals with classical and quantum descriptions of particles that interact with smooth random potentials, for example ultracold atoms in the dipole potential of an optical speckle pattern. In addition, a discussion of the link…
Particular solutions of the Benney equations are constructed. Their properties are discussed.
We give a simple rigourous treatment of the classical results of the abelian sandpile model. Although we treat results which are well-known in the physics literature, in many cases we did not find complete proofs in the literature. The…
We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of…
We present an expository account of the Bushell-Okrasi\'nski inequality, the motivation behind it, its history, and several generalizations. This inequality originally appeared in studies of nonlinear Volterra equations but very soon gained…
We add here compared to our former arXiv version an explicit expression for the descendant ratio along the generations The equation that is added here appeared in the Hebrew version published in BDD, Bar Ilan University Press, 23, 71, 2010,…
We pursue research leading towards the nature of causality in the universe. We establish the equation of the universe's evolution from the universe-state function and its series expansion, in which causes and effects connect together to…
Bethe-Salpeter equation is applied to nucleon-nucleon elastic scattering at the intermediate energy. The differential cross section and the polarization are calculated in terms of the phase shift analysis method using the two-body potential…
We solve the Bethe-Salpeter equation for two-particle scattering in a field-theoretical model using two lagrangians related by a field transformation. The kernel of the equation consists of the sum of all tree-level diagrams for each…
In this paper we present a possible origin of dark matter and dark energy from a solution of the Einstein's equation to a primordial universe, which was presented in a previous paper. We also analyze the Dirac's equation in this primordial…
Je retracerai l'histoire des conjectures de Weil sur le nombre de solutions d'\'equations polynomiales dans un corps fini et quelques unes des approches qui ont \'et\'e propos\'ees pour les r\'esoudre. The Weil conjectures: origins,…
Some remarks on the jump condition appearing in Theorems 1.1 and 1.2 in the article [1] and their implications are given.
The purpose of this article is to describe the two approaches to compute exact formulas (which are amenable to asymptotic analysis) for the probability distribution of the current of particles past a given site in the asymmetric simple…
This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon…
This is an introductory document surveying several results in polynomial approximation, known as the Bramble-Hilbert lemma.
This article relates two topics of central importance in modern astronomy - the discovery some fifteen years ago of the first planets around other stars (exoplanets), and the centuries-old problem of understanding the origin of our own…
We present an elementary proof for Ljunggren equation
Since its introduction in 1650, Kepler's equation has never ceased to fascinate mathematicians, scientists, and engineers. Over the course of five centuries, a large number of different solution strategies have been devised and implemented.…
We study the theory of equations in one variable over polyhedral semirings. The article revolves around a notion of solution to a polynomial equation over a polyhedral semiring. Our main results are a characterisation of local solutions in…
The goal of this chapter is to review hypotheses for the origin of the Pluto system in light of observational constraints that have been considerably refined over the 85-year interval between the discovery of Pluto and its exploration by…