Related papers: The many body problem in relativistic quantum mech…
For the calculation of the partition function $\mathcal{Z}$ of small, isolated and interacting many body systems an improvement with respect to previous formulations is presented. By including anharmonicities and employing a variational…
A particulare case of the three-body problem, in the PPN formalism, is presented. The Hamiltonian function is obtained and the problem is reduced to a perturbed two-body one.
We address the question to what extent the centre-of-mass (COM) separation can change our view of the many-body problem in quantum chemistry and solid state physics. It was shown that the many-body treatment based on the…
We consider the 3-body problem in relativistic lineal gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly-bound orbits of higher frequency compared to…
We consider $n$-body problems given by potentials of the form ${\alpha\over r^a}+{\beta\over r^b}$ with $a,b,\alpha,\beta$ constants, $0\le a<b$. To analyze the dynamics of the problem, we first prove some properties related to central…
A solution of the n-body problem in R^d is a relative equilibrium if all of the mutual distance between the bodies are constant. In other words, the bodies undergo a rigid motion. Here we investigate the possibility of partially rigid…
We analyze the occurrence of dynamically equivalent Hamiltonians in the parameter space of general many-body interactions for quantum systems, particularly those that conserve the total number of particles. As an illustration of the general…
The variational method in a reformulated Hamiltonian formalism of Quantum Electrodynamics is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels…
We derive a Hamiltonian for an extended spinning test body in a curved background spacetime, to quadratic order in the spin, in terms of three-dimensional position, momentum, and spin variables having canonical Poisson brackets. This…
A quantum mechanical three-body problem for two identical fermions of mass $m$ and a distinct particle of mass $m_1$ in the universal limit of zero-range two-body interaction is studied. For the unambiguous formulation of the problem in the…
An approximate quantum-mechanical two-body equation for spinless particles incorporating relativistic kinematics is derived. The derivation is based on the relativistic energy-momentum relation $mc^{2}+\epsilon =…
The classical formalism of the Moment Problem has been combined with a cumulant approach and applied to the extensive many-body problem. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the…
A summary is given of some results and perspectives of the hamiltonian ADM approach to 2+1 dimensional gravity. After recalling the classical results for closed universes in absence of matter we go over the the case in which matter is…
We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of…
An approach is developed to find approximate solutions to the classical Newtonian problem of N bodies. Sets of N gravitating bodies having spherically symmetric mass distributions, small angular velocities (< 1 rad/s) and bounded position…
A new formulation of relativistic quantum mechanics is presented and applied to a free, massive, and spin zero elementary particle in the Minkowski spacetime. The reformulation requires that time and space, as well as the timelike and…
An improved hyperspherical harmonic method for the quantum three-body problem is presented to separate three rotational degrees of freedom completely from the internal ones. In this method, the Schr\"{o}dinger equation of three-body problem…
In this note we discuss the quantum mechanical three-body problem with pairwise zero-range interactions in dimension three. We review the state of the art concerning the construction of the corresponding Hamiltonian as a self-adjoint…
The scattering and bound states of the many-body systems, related to the short-range Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a…
We prove for a large class of n-body problems including a subclass of quasihomogeneous n-body problems, the classical n-body problem, the n-body problem in spaces of negative constant Gaussian curvature and a restricted case of the n-body…