Related papers: Bethe-Salpeter Equation -- The Origins
There is a need for covariant solutions of bound state equations in order to construct realistic QCD based models of mesons and baryons. Furthermore, we ideally need to know the structure of these bound states in all kinematical regimes,…
Baxter's $T-Q$ relation for the periodic spin-$\frac12$ XYZ chain is studied. We extensively perform numerical calculations for the $T-Q$ relation and the Bethe ansatz equations. Numerical based hypotheses are then proposed to answer some…
We present a fascinating model that has lately caught attention among physicists working in complexity related fields. Though it originated from mathematics and later from economics, the model is very enlightening in many aspects that we…
The origin of the highly eccentric, inclined, and resonance-locked orbit of Pluto has long been a puzzle. A possible explanation has been proposed recently [Malhotra, R., {\it Nature} 365:819-21 (1993)] which suggests that these…
In a recent paper by N. Santowsky et al. [Phys. Rev. D 102, 056014 (2020)], covariant coupled equations were derived to describe a tetraquark in terms of a mix of four-quark states $2q 2\bar{q}$ and two-quark states $q\bar{q}$. These…
This paper gives a self-contained, elementary, and largely pictorial statement of Einstein's equation.
Motivated by the observation of a recent renewal of rather strong interest in the description of bound states by (semi-) relativistic equations of motion, we revisit, for the example of the Woods-Saxon interactions, the eigenvalue problem…
We develop an advanced method of solving homogeneous and inhomogeneous Bethe-Salpeter equations by using the expansion over the complete set of 4-dimensional spherical harmonics. We solve Bethe-Salpeter equations for bound and scattering…
In these lectures the introduction to algebraic aspects of Bethe Ansatz is given. The applications to the seminal spin 1/2 XXX model is discussed in detail and the generalization to higher spin as well as XXZ and lattice Sine-Gordon model…
This paper extends the work of Clarke [1] on the Bayesian foundations of the biomagnetic inverse problem. It derives expressions for the expectation and variance of the a posteriori source current probability distribution given a prior…
This technical note describes a new baseline for the Natural Questions. Our model is based on BERT and reduces the gap between the model F1 scores reported in the original dataset paper and the human upper bound by 30% and 50% relative for…
In this article, we provide a modified argument for proving the conditional stability of inverse source problem for a hyperbolic equation. Our method does not require any extension of solution with respect to time and therefore simplifies…
An informal guide to the history of Heisenberg's matrix mechanics. It is designed for mathematicians with only a minimal background in either physics or geometry, and it is based upon Heisenberg's original arguments.
In the last 40 years the study of initial boundary value problem for the Korteweg-de Vries equation has had the attention of researchers from various research fields. In this note we present a review of the main results about this topic and…
This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…
In this fact sheet we give some preliminary research results on the Bayesian Decision Theory. This theory has been under construction for the past two years. But what started as an intuitive enough idea, now seems to have the makings of…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
We propose a scenario for the origin of life based on the coevolution of lipid bilayer vesicles and protein channels.
The instantaneous formulations for the relativistic Bethe-Salpeter (BS) and the radiative transitions between the bound-states are achieved if the BS kernel is instantaneous. It is shown that the original Salpeter instantaneous equation set…
This article reviews from one point of view the current status of the manifestations of isotope effect in a nuclear, atomic and molecular as well as solid state physics. Although these manifestations vary, they have one common feature -…