Related papers: Normalization of the covariant three-body bound st…
The renormalization conditions of inhomogeneous systems of a quantum field under an external potential are studied, for both equilibrium and nonequilibrium scenarios and based on Thermo Field Dynamics. Extending the concept of the on-shell…
A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the…
We present a systematically improvable method for numerically solving relativistic three-body integral equations for the partial-wave projected amplitudes. The method consists of a discretization procedure in momentum space, which…
In relativistic frameworks, given by the Bethe-Salpeter and light-front bound state equations, the binding energies of system of three scalar particles interacting by scalar exchange particles are calculated. In contrast to two-body…
We perform a renormalization group analysis of the non-relativistic four-boson problem by means of a simple model with pointlike three- and four-body interactions. We investigate in particular the unitarity point where the scattering length…
In quantum theory, bound states are described by eigenvalue equations, which usually cannot be solved exactly. However, some simple general theorems allow to derive rigorous statements about the corresponding solutions, that is, energy…
The problem of calculating of the mass spectrum of the two-body Bethe-Salpeter equation is studied with no reduction to the three-dimensional ("quasipotential") equation. The method to find the ground state and excited states for a channel…
The subject of this paper is the consecutive procedure of discretization and quantization of two similar classical integrable systems in three-dimensional space-time: the standard three-wave equations and less known modified three-wave…
This talk reviews several aspects of the "semirelativistic" description of bound states by the spinless Salpeter equation (which represents the simplest equation of motion incorporating relativistic effects) and, in particular, presents or…
For two bound-state equations derived as simplified forms of the Bethe-Salpeter equation with confining interaction, stability of all solutions is rigorously shown.
We investigate the renormalization group theory of generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by…
The two-body Dirac equations for the bound q bar q systems are obtained from the different (five) versions of the 3D-equations derived from Bethe-Salpeter equation with the instantaneous kernel in the momentum space using the additional…
A discrete class of privileged reference frames in a closed universe with identical equations of motion for physical degrees of freedom was found. A representation of the quantum state of the universe in a privileged reference frame was…
We consider renormalization of the three-body scattering problem in low-energy effective field theory of self-interacting scalar particles by applying time-ordered perturbation theory to the manifestly Lorentz-invariant formulation. The…
Using as an example the Einstein gravity with the cosmological constant, we discuss the calculation of renormalization group functions off shell. We found, that gauge dependent terms should be absorbed by the nonlinear renormalization of…
The bound state Bethe-Salpeter amplitude was expressed by Nakanishi in terms of a smooth weight function g. By using the generalized Stieltjes transform, we derive an integral equation for the Nakanishi function g for a bound state case. It…
We discuss renormalization of the non-relativistic three-body problem with short-range forces. The problem is non-perturbative at momenta of the order of the inverse of the two-body scattering length. An infinite number of graphs must be…
Continuing work initiated in an earlier publication [H. Asada, Phys. Rev. D {\bf 80}, 064021 (2009)], the gravitational radiation reaction to Lagrange's equilateral triangular solution of the three-body problem is investigated in an…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
We present a quantization condition for the spectrum of a system composed of three identical bosons in a finite volume with periodic boundary conditions. This condition gives a relation between the finite volume spectrum and infinite volume…