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A new formalism for the description of the two-body system and well suited to the bound-state problem is developed within the context of quantum electrodynamics. The resulting two-body equation is a two-time, covariant, functional-differential one which, in the center-of-mass frame, reduces to a single-time, Schrodinger-type equation. Application of this equation is illustrated by calculating several known recoil and structure corrections to the energy levels of positronium and hydrogen. Further extensions and applications of the formalism are discussed.

The new bound-state formalism developed previously is here extended in two important respects. First is the inclusion of self-energy effects and the demonstration of the implementability of the usual renormalization procedure by means of a calculation of the lowest-order self-energy effects comprising the Lamb shift in a hydrogenlike atom. Second is the derivation of the two-body equation for the particle-antiparticle case where annihilation effects enter. This is exemplified by the derivation of the positronium equation and a calculation of a (known) annihilation contribution to its singlet-triplet splitting. The entire development is facilitated by a modified functional formulation which chooses the fully interacting physical system as the unperturbed one. (AIP)

A class of solutions of Einstein's gravitational field equations is discussed which describes the collapse or expansion of a charged, perfect-fluid spherical distribution of matter. These solutions reduce in the appropriate limits to certain charged Newtonian polytropes. A physical interpretation of the collapsing configurations is given, and it is shown that these solutions can describe the gravitational collapse of a bounded, charged fluid around a charged black hole. In all these configurations the singular region is either a spacelike or a null hypersurface. Therefore, the final state of collapse cannot be described by the complete analytic extension of the Reissner-Nordstr\"om spacetime. The special case of uniform density models is investigated in detail and it is shown that they describe the accretion of neutral matter by a charged black hole. On the basis of this analysis, it is suggested that for the realistic collapse of charged matter the singular region formed within the matter is either spacelike or null.

An analysis of two-dimensional, massless SU(N) Yang-Mills theory initiated previously is continued and extended. The fermion propagator in the presence of a non-Abelian potential is constructed exactly, and the corresponding (induced) vacuum fermion currents and their divergences are deduced. The analysis of the color-singlet current and the associated bound states reveals the nonexistence of massive color-singlet bound states. This fact, together with the previously established existence of massive ''colored'' states, characterizes the spectrum, save for possible massless excitations. A consideration of the boson-representation version of the theory reveals the symmetry breaking and the associated mass generation to be a Schwinger-type mechanism. An Abelian model illustrating this analogy is briefly analyzed and discussed.

We consider spacetimes with a perfect fluid distribution characterized by the energy density $\ensuremath{\mu}$, pressure $p$, charge density $\ensuremath{\zeta}$, and an equation of state $p=p(\ensuremath{\mu})$, or $p\ensuremath{\equiv}0$. It is shown that the only nonstatic isotropic solution of the Einstein-Maxwell equations where the contraction or expansion of the matter is shear free and the equation of state is physically reasonable is the Friedmann-Lema\^{\i}tre-Robertson-Walker class of solutions. Moreover, this conclusion holds for neutral matter even when the assumption of isotropy is replaced by the weaker hypothesis of irrotational motion.

A general formulation is given for the derivation of relativistic equations and associated potentials describing the field-theoretical interaction of two or more particles using a recently developed functional, field-theoretical formalism. The latter allows an exact single-time treatment which makes possible a global (i.e., off-shell) definition of the potential as a certain set of ''connected'' contributions. The potential thus obtained is a nonlocal operator with a precisely defined energy dependence. Simple, illustrative applications to N-electron and N-nucleon systems are given, and the one-boson exchange and annihilation potentials for the nucleon-antinucleon system are calcualted. The one-boson annihilation contribution is shown to be quite important. Remarks concerning the applicability of the formalism as well as extension to non-Abelian gauge theories are presented.

It is shown that gravitationally collapsed bounded systems which are too massive to be supported by their pressure may be held in equilibrium by self-induced magnetic stresses. A three-parameter family of solutions of the static axisymmetric interior Einstein-Maxwell equations is derived which describes matter distributions that are solely balanced by magnetic forces. The mass and the magnetic moment associated with these systems are then determined directly from the exterior field equations and the appropriate fluxes at the boundary of each system's interior. Some physical implications of the derived solutions - none of which contain a singularity or an event horizon - have also been discussed.

A formulation is presented for the derivation of a Schr\"odinger-equation potential from a field-theoretical model. The relativistic two-body equation of Bethe and Salpeter is reduced using a generalization of the Blankenbecler-Sugar method. The resulting equation is shown to be identical with the nonrelativistic Lippmann-Schwinger equation upon a unitarity-preserving identification of the amplitudes. An equivalent potential is thereby defined and expressed as a solution of an integral equation. The second- and fourth-order potentials are calculated, and their energy dependence and nonlocality are studied. An approximation scheme is developed for expanding the configuration-space potentials in the powers of the momentum operator. Terms up to and including the first power are retained, giving rise to a potential composed of central, spin-orbit, tensor, and spin-spin parts. The contributions of the meson resonances $\ensuremath{\eta}$, $\ensuremath{\rho}$, and $\ensuremath{\omega}$ are included to second order. The complete potential is numerically calculated using masses and coupling parameters taken from meson experiments; no parameter of the potential is searched upon. The resulting potential is remarkably similar to that of Hamada and Johnston (outside half a pion Compton wavelength), particularly for the parts that are relatively well determined by nucleon-nucleon scattering data. Further extensions of the program, including the treatment of the nucleon resonances and pair suppression, are discussed, and an outline of such extensions is given.

A contradictory result recently reported for canonical quantization in the temporal gauge, and claimed to render the validity of the quantization procedure itself doubtful, is shown to be incorrect and the result of the application of a nonexistent Hermiticity property with respect to the unphysical degrees of freedom of the gauge field.

The results of Nutt and Wilets are interpreted as substantiating the accuracy of the simultaneous local and energy-independent approximations for intermediate- and long-range potentials.

A nucleon-nucleon interaction potential is derived which includes all exchanges between a pair of nucleons involving a single $\ensuremath{\sigma}$ meson and any number of pion-pair inserts on the $\ensuremath{\sigma}$-meson propagator and vertices. The reduction of the Bethe-Salpeter kernel to a potential follows the method of Partovi and Lomon. The $\ensuremath{\sigma}$-pion and $\ensuremath{\sigma}$-nucleon couplings are restricted by the Adler chiral condition at zero four-momentum transfer, renormalized. The $\ensuremath{\sigma}$-meson mass is taken from experimental evidence to be nearly ${M}_{\ensuremath{\rho}}$. Various $\ensuremath{\sigma}$-meson widths are considered. Widths greater than 300 MeV predict small $\ensuremath{\sigma}$-meson contributions to the potential due to persistent cancellations between graphs. In particular near the width of about 610 MeV predicted by Weinberg's asymptotic restrictions the $\ensuremath{\sigma}$-potential contribution is a minimum and nearly cancels the familiar one-plus-two nucleon-pair contribution to the potential. The corrections to the previously obtained single-pion, $\ensuremath{\eta}\ensuremath{-}$, $\ensuremath{\rho}\ensuremath{-}$, and $\ensuremath{\omega}\ensuremath{-}$ meson and two-pion potentials are such as to increase the resemblance to Hamada-Johnston and Reid potentials or increase the resemblance to the Feshbach-Lomon potential for $\ensuremath{\sigma}$-meson widths near 620 MeV and 660 Mev, respectively.