Spin precession in the relativistic two-body problem

Synge's approximation procedure is applied to calculate the spin precession of either body in a binary system consisting of two rotating, spherical, rigid bodies of comparable mass and radius. The calculations are valid for the case in which the mass-radius ratio of each body, as well as the ratio of the radius of either body to the distance between their centers, is small. The results agree with those of earlier authors, who use different techniques, except for a term that arises from the effect of the rotation on the stress within the bodies. This term is similar in form to the quadrupole term of Barker and O'Connell, which they obtain when they allow the bodies to become distorted under the influence of the rotation.     

Orbital equations in the relativistic two-body problem

Synge's approximation method is applied to derive the orbital equations for a binary system consisting of two rotating, spherical, rigid bodies of comparable mass and radius. Approximations are based on the weakness of the field and on the distance between the bodies being considered large by comparison with their radii.     

Classical and quantum two-body problem in general relativity

The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the linearized quantum theory of gravity. It reduces to a Schwarzschild-like potential with two different Schwarzschild radii. The results derived in a weak field approximation are expected to be relevant for relativistic velocities.Revised version of Trieste preprint IC/80/124 (August 1980).A similar approach is being developed by a number of authors (see, e.g., References [9] and [10]); the reader will find a comprehensive bibliography in References [11] and [8].     

The Brillouin-Wigner expansion in a relativistic two-body formalism

The Brillouin-Wigner perturbation theory is used to precisely calculate the energy levels of hydrogen-like systems.     

The axially-symmetric two-body problem

A new approach to the two-body problem is introduced which entails the perturbation of an initially static configuration. It is demonstrated that Einstein's theory demands that the bodies move when the equilibrium-sustaining stress is weakened. Radiation from the system, both during the stress-breaking and free-fall period are discussed. For free-fall, the non-linearities could greatly alter the energy loss rate from that predicted by the ‘quadrupole formula’.     

Equivalent two-body potentials

The consequences of the existence of a bound state in a local nuclear two-body potential for charge distribution, inelastic scattering, photodisintegration and saturation are investigated.     

An existence proof for the Hartree-Fock time-dependent problem with bounded two-body interaction

Using fixed point theorems for local contractions in Banach spaces, an existence and uniqueness proof for the Hartree-Fock time-dependent problem is given in the case of a finite Fermi system interacting via a bounded two-body potential. The existence proof for the “strong” solution of the evolution problem is obtained under suitable conditions on the initial state.     

The time-dependent Hartree-Fock equations with Coulomb two-body interaction

The existence and uniqueness of global solutions to the Cauchy problem is proved in the space of smooth density matrices for the time-dependent Hartree-Fock equations describing the motion of finite Fermi systems interacting via a Coulomb two-body potential.On leave of absence from Mathematics Department, Indiana University, Bloomington, Indiana 47401, USA.     

The electromagnetic two-body problem in special relativity

A system of two point charged particles is considered. Each particle moves in the electromagnetic field created by the other particle according to Maxwell's equations. A scheme of successive approximations is developed to study the field and the motion of the charges. The field (potentials and intensities) are exapanded in powers of c^?1 using a retarded time coordinate. The variables of the motion (position vectors, velocities, etc) are expanded in powers of c^?1 with coefficients depending on t only. The field is evaluated in the first three approximations. The equations of motion are derived in the same approximations and the corresponding conserved quantities are explicitly given. Thus, the usual assumption of an action-at-a-distance principle is avoided and the original nonlinear integrodifferential equations are reduced to a sequence of linear equations.     

The field theory two-body problem in acoustics

We address the problem of determining effective equations of motion for sources in field theories, where finite propagation speeds lead to radiation reaction and runaway solutions. Acoustics is used to illustrate a solution of this problem: The effective equation of motion is obtained by reduction to an inertial manifold. This equation can be approximated to any desired accuracy by expansion (and truncation) in powers of the reciprocal of the wave propagation speed and reduction to a slow manifold of a singular perturbation problem. This research is supported by a grant from the National Science Foundation NSF DMS-0604331.     

The two-body multipole problem of electrodynamics

A 2-body system composed of two objects having arbitrary distributions of charge and current is discussed. An expression for the velocity dependent potential between these two objects has been obtained in the non-relativistic approximation. This potential consists of two parts viz. a velocity independent scalar potential Φ_eff and another part which is linearly dependent on the relative velocity between the objects. The second part naturally suggests a vector potential A_eff. The potentials have been expanded into multipole terms. It has been found that Φ_eff is a sum of two components viz. Φ_EE and Φ_MM such that each multipole term in Φ_EE represents an interaction between the electric multipoles of the two systems, each term in Φ_MM represents an interaction between their magnetic multipoles whereas each term in A_eff represents an interaction between an electric multipole of one and a magnetic multipole of the other. The results have been applied to the interaction between an electric dipole and a magnetic dipole. The symmetry among the multipole terms in A_eff suggests vanishing vector potential between two identical objects. A corollary of this appears to be absence of spin orbit interaction between two identical particles in the same spin state.     

Classical limits for quantum particles in external Yang-Mills potentials

We consider the limit ?→0 for nonrelativistic quantum particles moving in external Yang-Mills potentials. It is shown that the partition function and the solutions of the equations of motion converge to their corresponding classical counterparts.     

The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual $\text{N}\text{N}$ loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.     

Pion chemical potentials in heavy-ion collisions: relativistic quantum molecular dynamic analysis

In the framework of relativistic quantum molecular dynamics we analyse pion chemical potentials in the hadron system produced in central heavy-ion collisions at the bombarding energiesE _lab/A=(1–2) GeV/nucl. We find that the equilibrium relations hold for chemical potentials of π^?, of π⁰, of π⁺ and pion energy spectra reach local thermal equilibrium. However, there is no chemical equilibrium. The pion chemical potentials are very large and decrease during the expansion stage.     

The two-body problem in Rosen's bimetric theory of gravitation

This is a continuation of a previous paper, in which the field equations in successive approximations and the post-Newtonian equations of motion in Rosen's theory of gravitation were derived. In this paper the energy integral and the center of mass for an insular system with an arbitrary structure are obtained in the post-Newtonian approximation. A many-body system is considered, and in the extreme case of point bodies (particles) the center-of-mass coordinates are found to be identical with the Einsteinian ones. The two-body problem is considered. For a system of two identical neutron stars of mass 1.3M (a possible model of the Hulse-Taylor binary pulsar system) the trajectory and the perihelion precession are calculated. It is found that the expressions obtained depend on the gravitational self-energy of the stars. The relations deduced from Rosen's bimetric gravitation in the case of small velocities and weak fields are compared with those of general relativity.In partial fulfillment of the requirements for Dr.Sc. degree at the Technion-Israel Institute of Technology.