Related papers: Classical Grand Angular Momentum in N-Body Problem…
We prove a lower bound for the modulus of the amplitude for a two-body process at large scattering angle. This is based on the interplay of the analyticity of the amplitude and the positivity properties of its absorptive part. The…
Extra dimensions can be utilized to simplify problems in classical mechanics, offering new insights. Here we show a simple example of how the motion of a test particle under the influence of an inverse-quadratic potential in 1D is…
These notes contain a presentation of the noncommutative generalization of the classical moment problem introduced in [10] and [12]. They also contain a short summary of the classical moment problem in infinite dimension.
We compute the four-momentum radiated during the scattering of two spinless bodies, at leading order in the Newton's contant $G$ and at all orders in the velocities, using the Effective Field Theory worldline approach. Following…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
Within a scalar model theory of gravity, where the interaction between particles is given by the half-retarded + half-advanced solution of the scalar wave equation, we consider an N-body problem: we investigate configurations of N particles…
We consider several $N$-body problems. The main result is a very simple and natural criterion for decoupling the Jacobi equation for some classes of them. If $E$ is a Euclidean space, and the potential function $U(x)$ for the $N$-body…
This article serves as a pedagogical introduction to the problem of motion in classical field theories. The primary focus is on self-interaction: How does an object's own field affect its motion? General laws governing the self-force and…
Procedures for projecting angular momentum in a model describing a hot nucleus that takes into account large-amplitude quadrupole fluctuations are discussed. Particular attention is paid to the effect angular-momentum projection has on the…
In a previous paper we treated within the framework of our Projective Unified Field Theory (Schmutzer 2004, Schmutzer 2005a) the 2-body system (e.g. earth-moon system) with a rotating central body in a rather abstract manner. Here a…
Giant Resonances are, with nuclear rotations, the most evident expression of collectivity in finite nuclei. These two categories of excitations, however, are traditionally described within different formal schemes, such that vibrational and…
We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on…
Construction of the microscopic theory of large-amplitude collective motion, capable of describing a wide variety of quantum collective phenomena in nuclei, is a long-standing and fundamental subject in the study of nuclear many-body…
A simple approach for understanding the quantum nature of angular momentum and its reduction to the classical limit is presented based on Schwinger's coupled-boson representation. This approach leads to a straightforward explanation of why…
We investigate systems of three mutually interacting particles with masses of which the inner is much bigger than the intermediate and the latter is much bigger than the outer. Then the three-body problem reduces to the two-body scattering…
We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…
Our idea is to imitate Smale's list of problems, in a restricted domain of mathematical aspects of Celestial Mechanics. All the problems are on the n-body problem, some with different homogeneity of the potential, addressing many aspects…
The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for…
The coupled dynamics of the scissors mode and the isovector giant quadrupole resonance is studied in a model with separable quadrupole-quadrupole residual interactions. The method of Wigner function moments is applied to derive the…
The Schr\"odinger equation for two and tree-body problems is solved for scattering states in a hybrid representation where solutions are expanded in the eigenstates of the harmonic oscillator in the interaction region and on a finite…