arXiv subjects
Publications and source records attributed to M. Mangin-Brinet.
We show that in the system of two fermions interacting by scalar exchange, the solutions for J$^π$=$0^+$ bound states are stable without any cutoff regularization, for values of the coupling constant $α$ below a critical value $α_c$. This latter is calculated from an eigenvalue equation.
The bound state solutions of two fermions interacting by a scalar exchange are obtained in the framework of the explicitly covariant light-front dynamics. The stability with respect to cutoff of the J$^π$=$0^+$ and J$^π$=$1^+$ states is studied. The solutions for J$^π$=$0^+$ are found to be stable for coupling constants $α={g^2\over4π}$ below the critical value $α_c\approx 3.72$ and unstable above it. The asymptotic behavior of the wave functions is found to follow a ${1\over k^{2+β}}$ law. The coefficient $β$ and the critical coupling constant $α_c$ are calculated from an eigenvalue equation. The binding energies for the J$^π$=$1^+$ solutions diverge logarithmically with the cutoff for any value of the coupling constant. For a wide range of cutoff, the states with different angular momentum projections are weakly split.
Some of the last results on low energy antiproton physics are reviewed. First Faddeev calculations for nd scattering length are presented.
We show that in the system of two fermions interacting by scalar exchange, the solutions for J$^π$=$0^+$ bound states are stable without any cutoff regularization for coupling constant below some critical value.
Light-front dynamics (LFD) is a powerful approach to the theory of relativistic composite systems (hadrons in the quark models and relativistic nucleons in nuclei). Its explicitly covariant version has been recently applied with success to describe the new CEBAF/TJNAF data on the deuteron electromagnetic form factors. The solutions used in were however not obtained from solving exactly the LFD equations but by means of a perturbative calculation with respect to the non relativistic wave function. Since, a consequent effort has been made to obtain exact solutions of LFD equations. The first results concerning J=0 states in a scalar model have been published in nucl-th/9912050. The construction of $J \ne 0$ states in LFD is complicated by the two following facts. First, the generators of the spatial rotations contain interaction and are thus difficult to handle. Second, one is always forced to work in a truncated Fock space, and consequently, the Poincaré group commutation relations between the generators -- ensuring the correct properties of the state vector under rotation -- are in practice destroyed. In the standard approach, with the light-front plane defined as $t+z=0$, this violation of rotational invariance manifests by the fact that the energy depends on the angular momentum projection on $z$-axis. We present here a method to construct $J\ne0$ states in the explicitly covariant formulation of LFD and show how it leads to a restoration of rotational invariance.
We show some results concerning the weak binding limit for J=0 states -- which turn out to strongly differ from the non relativistic case -- together with the construction of non zero angular momentum states. The calculation of such states in the Light-Front Dynamics (LFD) framework has some peculiarities which are absent in other approaches. They are related to the fact that the rotation generators contain interaction. We present here the construction of non zero angular momentum states in LFD and show how it leads to a restoration of rotational invariance. For this purpose, the use of Light-Front Dynamics in its explicitly covariant formulation is of crucial importance since the dependence of the wave function on the light-front plane is explicitly parametrized.
Exact boundary conditions at finite distance for the solutions of the time-dependent Schrodinger equation are derived. A numerical scheme based on Crank-Nicholson method is proposed to illustrate its applicability in several examples.