The N*(1710) contribution to the Θ+ production cross sections in p-p collisions

In this paper we derive the Θ production cross section in high energy proton-proton collisions in the relativistic framework through using effective hadronic couplings. Both the nucleon and N^*(1710) propagations are taken into account in the intermediate states. The one π and one ρ exchange mechanisms are considered and the commonly accepted coupling constants and form factors are used in the calculation. We find that ρ exchange is dominant in these processes and the N^*(1710) propagation in the intermediate state is important,which increases the Θ production cross section by a factor of a few tens at center of mass energy 4GeV.     

LOCV calculation of nuclear matter with relativistic Hamiltonian

The equation of state of symmetric nuclear matter is calculated using the relativistic Hamiltonian (H_R) with potentials which have been fitted with the N -N scattering data using the relativistic two-body Hamiltonian ( [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and the non-relativistic two-body Hamiltonian, i.e. the Argonne V₁₄ interaction. The boost interaction corrections as well as the relativistic one-body and two-body kinetic energy corrections in cluster expansion energy within the lowest-order-constrained variational method are calculated. It is shown that the relativistic corrections reduce the binding energy by 1.5MeV for [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and AV₁₄ interactions. The symmetric nuclear-matter saturation energy is about -16.43 MeV at r \rho = 0.253 (fm^-3) with [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} interaction plus relativistic corrections. Finally, various properties of the symmetric nuclear matter are given and a comparison is made with the other many-body calculations.     

Positive and Negative Mixtures in Relativistic Schrödinger Theory

The general formalism of relativistic Schrödinger theory (RST) is specialized to a scalar two-particle system with electromagnetic interactions (scalar helium atom). The set of dynamically allowed field configurations splits up into positive and negative mixtures and pure states. The static and spherically symmetric solutions are constructed by means of first-order perturbation theory for the case of an attractive Coulomb potential. The corresponding energy levels for the positive and negative mixtures resemble the emergence of ortho and para states in the conventional quantum theory. The associated energy eigenvalues predicted by the RST seem to undergo a certain kind of mixture degeneracy as the RST analog of the conventional exchange degeneracy. The charge densities of the positive mixtures assimilate, whereas the densities of the negative mixtures recede from one another. Thus, positive (negative) mixtures strongly resemble the bosonic (fermionic) matter of the conventional theory when the Pauli principle is applied.     

Masses of S and P wave mesons and pseudoscalar decay constants using a confinement scheme

In the framework of relativistic harmonic confinement model for quarks and antiquarks, the masses of S- and P-wave mesons and pseudoscalar decay constants from light flavour to heavy flavour sectors are computed. The residual two-body Coulomb interaction and the spin-dependent interaction of the confined one gluon exchange effects (COGEP) such as spin-spin and spin-orbit interactions are perturbatively incorporated with the confinement energy to get the respective vector-pseudoscalar meson mass differences. Here we employ the same parametrization and model parameters as used in a recent study of low-lying hadron masses and leptonic decay widths. The results are being compared with the values obtained from other theoretical models and the experimental values.     

Renormalized Hartree-Fock equations in a nuclear relativistic quantum field theory

Renormalized Hartree-Fock equations are derived for an infinite system of mesons and baryons in the framework of a relativistic quantum field theory. Direct and exchange diagrams in the baryon propagator are summed self-consistently to all orders, and the effects of occupied negative-energy states in the Dirac sea are included. The required counterterm subtractions are defined by conventional renormalization conditions, but they need not be evaluated explicitly. The result is a set of finite nonlinear integral equations for the baryon self-energy that includes vacuum fluctuation effects from virtual N$\text{N}$ pairs in the many-body wavefunction at finite density.     

Numerical calculation of the fidelity for the Kondo and the Friedel-Anderson impurities

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number N _eff of states. A plot of ln(F) versus N ∝ ln(N _eff ) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F) – ln(N _eff ) plot for the Kondo impurity diverges for large N _eff . On the other hand, the corresponding plot for the symmetric FA impurity saturates for large N _eff when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime.     

Dynamical relativistic corrections to the leptonic decay width of heavy quarkonia

We calculate the dynamical relativistic corrections, originating from radiative one-gluon exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of light-front dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J = 1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in , even in the charmonium sector. This is in contrast with the ongoing belief based on calculations in the non-relativistic limit. Consequences for the ability of several phenomenological potentials to describe these decays are described. Received: 6 December 2001 / Published online: 5 April 2002     

Problem of Interactions: Gravitational Interactions

Within the framework of a new approach to the problem of particles [1], gravitational interactions are considered. Interactions of this type are associated with the degeneracy of states of a relativistic bi-Hamiltonian system T _3,1 underlying the given approach. Within the framework of this approach, there is a clearly defined difference between the gravitation and the metric theory of space-time.     

The many-body problem with an energy-dependent confining potential

We consider systems of N bosons bound by two-body harmonic interactions, whose frequency depends on the total energy of the system. Such energy dependent confining interactions between the bosons yield remarkable properties of the many-body system. As the quantum numbers increase, the total energy cannot exceed a saturation energy, which is independent of the number of particles N. Moreover, the ground state energy increases with N. As a result, the density of states tends rapidly to infinity as N and/or the quantum numbers increase.     

Measurement of chemical potentials of systems with strong excluded volume interactions by computing the density of states

At high densities and low temperatures, the conventional Widom test particle method to compute the chemical potential of a system of particles with excluded volume interactions fails owing to bad statistics. A way to circumvent this problem is the use of expanded ensemble simulation techniques or thermodynamic integration. In this article, we will describe an alternative method to compute the chemical potential which is conceptually much easier, by computing the density of states of systems of N and N + 1 particles directly; and by performing a test particle simulation at very high temperature. The advantage of our technique is that the densities of states of the N and N + 1 particle system are computed in an ensemble in which particles can pass each other, resulting in a more efficient sampling. We will demonstrate our method not only for single particles but also for chain molecules with intramolecular interactions. By using an infinite temperature expansion and an extension of the density of states to very high energies, we will show that it is also possible to compute the chemical potential without having to compute the density of states for the N + 1 particle system.     

Magnetic moments of <Superscript>33</Superscript>Mg in the time-odd relativistic mean field approach

The configuration-fixed deformation constrained relativistic mean field approach with time-odd component has been applied to investigate the ground state properties of 33Mg with effective interaction PK1.The ground state of 33Mg has been found to be prolate deformed,β2=0.23,with the odd neutron in 1/2[330] orbital and the energy -251.85 MeV which is close to the data -252.06 MeV.The magnetic moment -0.9134 μN is obtained with the effective electromagnetic current which well reproduces the data -0.7456 μN se...     

Fragmentation of relativistic nuclei in peripheral interactions in nuclear track emulsion

The technique of nuclear track emulsions is used to explore the fragmentation of light relativistic nuclei down to the most peripheral interactions: nuclear “white” stars. A complete pattern of the relativistic dissociation of a 8B nucleus with target fragment accompaniment is presented. Relativistic dissociation ⁹Be → 2α is explored using significant statistics, and a relative contribution of ⁸Be decays from 0+ and 2+ states is established. Target fragment accompaniments are shown for relativistic fragmentation ¹⁴N → 3He +H and ²²Ne → 5He. The leading role of the electromagnetic dissociation on heavy nuclei with respect to breakups on target protons is demonstrated in all these cases. It is possible to conclude that the peripheral dissociation of relativistic nuclei in nuclear track emulsion is a unique tool to study many-body systems composed of the lightest nuclei and nucleons in the energy scale relevant for nuclear astrophysics. The text was submitted by the authors in English.     

Covariant Hamiltonian dynamics with negative-energy states

A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the point form relativistic Hamiltonian dynamics. Negative-energy states are introduced taking into account the restrictions imposed by a correct definition of the Poincaré group generators. We obtain nonpathological, manifestly covariant wave equations that dynamically contain the contributions of the negative-energy states. Auxiliary negative-energy states are also introduced, specially for studying the interactions of the hadronic systems with external probes.     

Note on the kinetic energy inequality leading to Lieb's negative ionization upper bound

The kinetic energy inequality is alternatively proved which yields Lieb's boundN < 2Z + 1 on the maximum negative ionization of an atom with nucleus chargeZ andN electrons when the kinetic energy operator is the nonrelativistic or relativistic magnetic Schrödinger operator. It is seen to follow from the free case where the vector potential vanishes. The proof applies to the Weyl quantized relativistic magnetic Schrödinger operator as well.Research partially supported by Grant-in-Aid for Scientific Research Nos. 04640141 and 05640165, Ministry of Education, Science and Culture, Japanese Government.     

A Proof of Haag-Swieca's Compactness Property for Elastic Scattering States

 It is proved that in any massive relativistic quantum field theory satisfying two-particle asymptotic completeness, all the bounded energy components in the elastic two-particle range of all subsets of states which are excitations of the vacuum state by uniformly bounded observables localized in a given finite region of spacetime are compact in the Hilbert space of states. This result, which is in agreement with Haag-Swieca's conjecture, is also given a more precise form in terms of the rate of decrease of the ``N–dimensional thickness' (or approximation number) of such sets of states when N tends to infinity. A similar computation, valid at arbitrarily high energies, is also given for the massive free-field case. Received: 7 February 2003 / Accepted: 5 April 2003 Published online: 13 May 2003 Communicated by H. Araki, D. Buchholz and K. Fredenhagen     

Stability and instability of relativistic electrons in classical electromagnetic fields

The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with Coulomb interactions. In addition there is an arbitrary classical magnetic field of finite energy. Despite the previously known facts that ordinary nonrelativistic matter with magnetic fields, or relativistic matter without magnetic fields, is already unstable when a, the fine structure constant, is too large, it is noteworthy that the combination of the two is still stableprovided the projection onto the positive energy states of the Dirac operator, whichdefines the electron, is chosen properly. A good choice is to include the magnetic field in the definition. A bad choice, which always leads to instability, is the usual one in which the positive energy states are defined by the free Dirac operator. Both assertions are proved here. This paper is dedicated to Bernard Jancovici on the occasion of his 65th birthday.     

Justification of relativistic Dirac-Hartree-Fock and configuration interaction

Before knowing that the relativistic Hamiltonian H does allow the existence of bounded states (H is unbounded from below and from above), the existence of SCF and beyond SCF solutions had to be assumed as an act of faith vindicated by consistent numerical results. A recent theorem showing the existence of such bounded states furnishes a rigorous framework for the relativistic theory of electronic bounded states.     

Resonance theory of decoherence and thermalization

We present a rigorous analysis of the phenomenon of decoherence for general N-level systems coupled to reservoirs. The latter are described by free massless bosonic fields. We apply our general results to the specific cases of the qubit and the quantum register. We compare our results with the explicitly solvable case of systems whose interaction with the environment does not allow for energy exchange (non-demolition, or energy conserving interactions). We suggest a new approach which applies to a wide variety of systems which are not explicitly solvable.     

NΩ and ΔΩ dibaryons in a SU(3) chiral quark model

The binding energy of the six-quark system with strangeness s = −3 is investigated under the chiral SU(3) constituent quark model in the framework of RGM. The calculations of the single NΩ channel with spin S = 2 and the single ΔΩ channel with spin S = 3 are performed. The results show that both systems could be dibaryons and the interaction induced by the chiral field plays a very important role on forming bound states in the systems considered. The phase shifts and scattering lengths in corresponding channels are also given.     

Spin-Dependent Bohm Trajectories for Pauli and Dirac Eigenstates of Hydrogen

The de Broglie-Bohm causal theory of quantum mechanics is applied to the hydrogen atom in the fully spin-dependent and relativistic framework of the Dirac equation, and in the nonrelativistic but spin-dependent framework of the Pauli equation. Eigenstates are chosen which are simultaneous eigenstates of the energy H, total angular momentum M, and z component of the total angular momentum M _z. We find the trajectories of the electron, and show that in these eigenstates, motion is circular about the z-axis, with constant angular velocity. We compute the rates of revolution for the ground (n=1) state and the n=2 states, and show that there is agreement in the relevant cases between the Dirac and Pauli results, and with earlier results on the Schrödinger equation.