Positronium is a two-body, leptonic, particle-antiparticle system which possesses self-annihilation channels not directly present in any system studied to date. These features make it ideal for the study of the relativistic, two-body problem in quantum electrodynamics. This review will focus on recent experimental advances in fundamental positronium research. In addition, a less detailed discussion of recent theoretical advances is outlined. The review also contains a fairly detailed historial introduction and a section discussing uses of positronium in research not related to tests of quantum electrodynamics.

The restrictions on elementary particle properties which can be derived from cosmological and astrophysical data are considered. The inverse relations between micro- and macrophysics are also discussed, in particular the origin of the baryon asymmetry of the universe.

A comprehensive survey and data collection of experimental results achieved from diffracting beams of light gases like H, D, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, and ${\mathrm{H}}_2$ from single-crystal surfaces (alkali halides, oxides, and graphite) is given, and it is shown that gas-surface diffraction is a valuable tool to get detailed information on the physical gas-surface potential: (a) From comparison of diffracted beam intensities with calculations in a corrugated hardwall approximation the periodic structure of the interaction potential is obtained together with information on the atomic structure at the surface. (b) From bound-state resonance investigations one gets information on the different terms of the gas-surface potential in Fourier expansion $v\left(r\right)\mathrm{} ={\Sigma }_G v_G\mathrm{}\left(z\right)\mathrm{}\exp \left(iG·R\right)$: the achieved spectrum of binding energies {$E_j$} can be used to construct the main term $v_{00}\mathrm{}\left(z\right)\mathrm{}$, whereas observed splitting of degenerate bound states allows evaluation of the strength of the periodic terms $v_{\mathrm{G}}\mathrm{}\left(z\right)\mathrm{}$. (c) from $E_j$ levels near the dissociation limit the constant $C_3$ of gas-surface long-range dispersion attraction can be determined. Finally, regarding the experimental results on $C_3$ and the potential well depth $D$, two semiempirical rules are established: $C_3=K_C·\alpha \frac{(\epsilon -1)}{(\epsilon +1)}$ and $D=K_D·\alpha \frac{(\epsilon -1)}{(\epsilon +1)}$. These rules allow the calculation of $C_3$ and $D$ from the static electric polarizability $\alpha$ of the atom, the optical dielectric constant $\epsilon$ of the solid, and the system-independent constants $K_C$, $K_D$ given in the text. Calculated values of $D$ for several gas-surface systems are given in a table.

The concept of the double-humped fission barrier of actinide nuclei has made possible an understanding of a vast amount of data on nuclear fission during the past decade. In this article the analysis of most available relevant data is reviewed, and a synthesis of the fission barrier parameters and their trends over the actinide region is built up. The sequence of the work begins with an outline (but not a critical discussion) of the theoretical foundation of the double-humped barrier, and this is followed by a full account of the nuclear reaction theory required to describe fission reactions within the concept of such a barrier. This reaction theory provides the theoretical tools for a quantitative understanding of a range of phenomena of such kinds as spontaneously fissioning isomers, their half-live and yields, vibrational resonances and narrower intermediate structure in fission cross sections, and the general trends and magnitudes of fission cross sections at excitation energies near the top of the fission barrier. The magnitudes and trends of fission barrier parameters and the level structure of highly deformed nuclei that are extracted from the data on these phenomena are discussed in the light of current concepts of nuclear structure. Also, the possibility of a three-humped and more complex barriers is reviewed.

A review of recent capture experiments which discusses polarized proton, polarized neutron, and alpha particle capture reactions is presented. The giant dipole resonance region is examined chiefly in terms of the information which can be obtained from angular distribution measurements. Experimental results regarding the relative transition matrix elements and their phases are shown to be quite well accounted for by the direct-semidirect reaction theory. Some of the new information obtained from such experiments in the case of the three and four-body problems is described. The utility of polarized capture for the study of M1 and E2 strength is exhibited by examples. Several cases are shown in which the E2 strength observed in light nuclei via p capture is accounted for by a purely direct E2 mechanism. The virtues of polarized neutron capture studies are explored, and the results of the first experiments are described. Alpha particle capture is compared with $p$ and $n$ capture. Fundamental differences in the reaction processes are described which can account for the relatively small $a_1$ coefficients observed in $n$ versus $p$ capture and lack of E1-E2 coherence observed in several $\alpha$-capture experiments.

The deuterium nucleus plays an important role in several branches of high-energy physics. We review its present status as a neutron source, a relativistic bound state, a collective six-quark state and a double scatterer.

A pedagogical discussion of the Yang-Mills quantum theory is presented. A somewhat unconventional description makes use of physical, quantum-mechanical ideas, rather than of formal, mathematical developments. The purpose is to highlight those aspects of the model which have been exposed in the last few years by semiclassical methods, but without using semiclassical approximations. This requires a careful treatment of the non-Abelian gauge symmetry present in the theory.

This paper is an introduction to the study of spontaneous symmetry breaking and topological classification of defects. The latter topic has aits foundation in the former one; both subjects requires some mathematics not familiar to many physicists: group action and homotopy theory. These mathematics are introduced from examples and their main results, to be used for physics, are explained. It is hoped that this paper will enable the non specialist to read the physics literature which has very recently appeared on topological classification of symmetry defects. Some appendices (A,C,D,F,G) gives more mathematical details; the other appendices (B,E,H) explain some applications to different fields of physics, while mesomorphic phases are treated in the text (${\mathrm{He}}^3$ superfluid phases have been treated by Mermin, 1979).

Dynamical processes in macroscopic systems are often approximately described by kinetic and hydrodynamic equations. One of the central problems in nonequilibrium statistical mechanics is to understand the approximate validity of these equations starting from a microscopic model. We discuss a variety of classical as well as quantum-mechanical models for which kinetic equations can be derived rigorously. The probabilistic nature of the problem is emphasized: The approximation of the microscopic dynamics by either a kinetic or a hydrodynamic equation can be understood as the approximation of a non-Markovian stochastic process by a Markovian process.

The state of Regge pion exchange calculations for high-energy reactions is reviewed. Experimental evidence is summarized to show that (i) the pion trajectory has a slope similar to that of other trajectories; (ii) the pion exchange contribution can dominate contributions of higher trajectories up to quite a large energy; (iii) many two-body cross sections with large pion contributions can be fit only by models which allow for kinematical conspiracy at $t=0\mathrm{}$. The theory of kinematic conspiracy is reviewed for two-body amplitudes, and calculations of the conspiring pion-Pomeron cut discussed. The author then summarizes recent work on pion exchange in Reggeized Deck models for multiparticle final states, with emphasis on the predictions of various models (with and without resonances) for phases of the partial wave amplitudes.

This review of the properties of leptons, mesons, and baryons is an updating of Review of Particle Properties, Particle Data Group [Phys. Lett. 75B (1978)]. Data are evaluated, listed, averaged, and summarized in tables. Numerous tables, figures, and formulae of interest to particle physicists are also included. A data booklet is available.

This paper is a subjective review of experimental progress in the field of continuous phase transitions over the last decade or so, and is based primarily upon the author's own work and experiences in the field.

This paper presents a pedagogical review of duality (in the sense of Kramers and Wannier) and its application to a wide range of field theories and statistical systems. Most of the article discusses systems in arbitrary dimensions with discrete or continuous Abelian symmetry. Globally and locally symmetric interactions are treated on an equal footing. For convenience, most of the theories are formulated on a $d$-dimensional (Euclidean) lattice, although duality transformations in the continuum are briefly described. Among the familiar theories considered are the Ising model, the $x-y$ model, the vector Potts model, and the Wilson lattice gauge theory with a $Z_N$ or $U\left(1\right)\mathrm{}$ symmetry, all in various dimensions. These theories are all members of a more general heirarchy of theories with interactions which are distinguished by their geometrical character. For all these Abelian theories it is shown that the duality transformation maps the high-temperature (or, for a field theory, large coupling constant) region of the theory into the low-temperature (small coupling constant) region of the dual theory, and vice versa. The interpretation of the dual variables as disorder parameters is discussed. The formulation of the theories in terms of their topological excitations is presented, and the role of these excitations in determining the phase structure of the theories is explained. Among the other topics discussed are duality for the Abelian Higgs model and related models, duality transformations applied to random systems (such as theories of a spin glass), duality transformations in the "lattice Hamiltonian" formalism, and a description of attempts to construct duality transformations for theories with a non-Abelian symmetry, both on the lattice and in the continuum.

The molecular hydrogens (${\mathrm{H}}_2$, ${\mathrm{D}}_2$, HD, etc.) form the simplest of all molecular solids. The combination of the light mass, small moment of inertia, weak interactions, and the quasi-metastable ortho-para species result in a fascinating low-temperature behavior that can be understood to a large extent from considerations of first principles. After discussing single molecule properties and intermolecular interactions we discuss in detail the ortho-para properties, conversion and diffusion. This is followed by a description of the crystal structures and the orientational ordering phenomena. The thermodynamic properties are reviewed. The article is concluded with a discussion of the translational ground state of the solid and the effect of the large zero-point motion on the solid state properties. A large number of data are collected in tables and graphs to provide a reference source.

The monitoring of a quantum-mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. This paper reviews the standard techniques for monitoring the oscillator, and introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator. The standard method for monitoring the oscillator is the "amplitude-and-phase" method (position or momentum transducer with output fed through a narrow-band amplifier). The accuracy obtainable by this method is limited by the uncertainty principle ("standard quantum limit"). To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak classical force, but which cannot provide good accuracy in determining its precise time dependence. This paper considers extensively a new type of quantum nondemolition measurement—a "back-action-evading" measurement of the real part $X_1$ (or the imaginary part $X_2$) of the oscillator's complex amplitude. In principle $X_1$ can be measured "arbitrarily quickly and arbitrarily accurately," and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force. The authors describe explicit Gedanken experiments which demonstrate that $X_1$ can be measured arbitrarily quickly and arbitrarily accurately. In these experiments the measuring apparatus must be coupled to both the position (position transducer) and the momentum (momentum transducer) of the oscillator, and both couplings must be modulated sinusoidally. For a given measurement time the strength of the coupling determines the accuracy of the measurement; for arbitrarily strong coupling the measurement can be arbitrarily accurate. The "momentum transducer" is constructed by combining a "velocity transducer" with a "negative capacitor" or "negative spring." The modulated couplings are provided by an external, classical generator, which can be realized as a harmonic oscillator excited in an arbitrarily energetic, coherent state. One can avoid the use of two transducers by making "stroboscopic measurements" of $X_1$, in which one measures position (or momentum) at half-cycle intervals. Alternatively, one can make "continuous single-transducer" measurements of $X_1$ by modulating appropriately the output of a single transducer (position or momentum), and then filtering the output to pick out the information about $X_1$ and reject information about $X_2$. Continuous single-transducer measurements are useful in the case of weak coupling. In this case long measurement times are required to achieve good accuracy, and continuous single-transducer measurements are almost as good as perfectly coupled two-transducer measurements. Finally, the authors develop a theory of quantum nondemolition measurement for arbitrary systems. This paper (Paper I) concentrates on issues of principle; a sequel (Paper II) will consider issues of practice.