The most important single attribute of noncovariant gauges is their ghost-free nature. Although noncovariant gauges have been an integral part of quantum field theory for many decades, their effectiveness in the quantization of non-Abelian theories and their broad range of applicability have only recently been appreciated by theorists at large. The purpose of this review is to explain and illustrate the essential characteristics of some typical noncovariant gauges, such as the axial gauge, the planar gauge, the light-cone gauge, and the temporal gauge. The author's aim is to acquaint the reader not only with the basic properties of these ghost-free gauges, but also with their deficiencies and advantages over covariant gauges, their computational idiosyncrasies, and their dominant areas of application.

The article reviews the two-dimensional Coulomb gas model and its connection to vortex fluctuations for a two-dimensional superfluid. The neutral and non-neutral versions of the Coulomb gas are discussed and the relation to an equivalent sine-Gordon field theory is given. The charge-unbinding picture is used to elucidate some essential properties of the Coulomb gas. Derivations of approximate renormalization equations are sketched and the phase transition for the neutral two-dimensional Coulomb gas is described. The Kosterlitz renormalization-group equations are reviewed in some detail. The vortex-Coulomb gas charge analogy is carefully explained. The connections between experiments for ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films and superconducting films and the neutral and non-neutral versions of the Coulomb gas are outlined using concepts like the universal jump and the Coulomb gas scaling relations. The properties of a dynamical version of the Coulomb gas, corresponding to vortex dynamics, are discussed and related to experiments. An analogy with Maxwell's equations in two dimensions is also given.

An attempt is made to develop a description of the multielectron quantum state responsible for the integral quantum Hall effect. One goal is to provide intuitive support for the very powerful and general argument of Laughlin that the theoretical relationship is insensitive to complicating details in the interior of the sample. The model the author uses is somewhat more realistic than heretofore in that it is three dimensional, does not ignore the atomic structure of the bulk matter, and does not use an effective-mass approximation. In order to treat the problem quantum mechanically, the complete system, including circuitry external to the system of interest, is replaced by a model closed system consisting of a finite number of electrons. In this model, states with a finite Hall current and voltage are metastable against decay caused by interactions outside the model, such as those with bulk matter excitations. Such states describe the true situation well only in the conductivity plateaus; between plateaus, there would be current flow between the Hall voltage probes corresponding to decaying states. Experimental constraints replace this transverse current by a voltage drop along the direction of current flow. The interactions between the electrons are expressed in terms of a self-consistent potential which gives an independent-particle description as a starting point, and residual interactions which are treated by perturbation theory. The self-consistent potential is found to be important in understanding the properties of the quantum state of the system, such as the existence of the plateaus in conductivity and how the electrons in the (effective) two-dimensional region come to equilibrium with the different Fermi levels in the voltage probes. To all finite orders of perturbation theory, the residual interactions are found not to alter the quantized Hall conductivity.

This paper surveys the magnetic flux effects in multiply connected conductors, both normal metals and superconductors. Discussion of these effects for hopping conduction on the dielectric side of the metal-insulator transition is presented also. The main emphasis in the review is on the modern theoretical picture of these phenomena and comparison of theoretical results with experimental data.

The theory of neutrino mixing and neutrino oscillations, as well as the properties of massive neutrinos (Dirac and Majorana), are reviewed. More specifically, the following topics are discussed in detail: (i) the possible types of neutrino mass terms; (ii) oscillations of neutrinos (iii) the implications of $\mathrm{CP}$ invariance for the mixing and oscillations of neutrinos in vacuum; (iv) possible varieties of massive neutrinos (Dirac, Majorana, pseudo-Dirac); (v) the physical differences between massive Dirac and massive Majorana neutrinos and the possibilities of distinguishing experimentally between them; (vi) the electromagnetic properties of massive neutrinos. Some of the proposed mechanisms of neutrino mass generation in gauge theories of the electroweak interaction and in grand unified theories are also discussed. The lepton number nonconserving processes $\mu \to e\gamma$ and $\mu \to 3e$ in theories with massive neutrinos are considered. The basic elements of the theory of neutrinoless double-$\beta$ decay are discussed as well. Finally, the existing data on neutrino masses, oscillations of neutrinos, and neutrinoless double-$\beta$ decay are briefly reviewed. The main emphasis in the review is on the general model-independent results of the theory. Detailed derivations of these are presented.

The development of a coherent field-emission electron beam has facilitated practical applications of electron holography. This paper reviews this field of growing importance, making special reference to the application of electron holography to current technological problems. It is seen that the phase distribution of an electron wave function transmitted through a specimen can be observed as an interference micrograph, thus providing considerable information about the microscopic distribution of electromagnetic potentials. For example, a magnetic sample's contour fringes directly indicate its magnetic lines of force. These fringes can also show the equipotential lines of an electric sample and thickness contours of a homogeneous specimen. Holographic techniques can be effectively employed to improve the accuracy of phase measurements up to an order of $\frac{2\pi }{100}$. This opens the way for use of electron holography as a high-precision measurement method that can cast light on wide regions of the microscopic world pertinent to both basic science and practical industry.

The first measurements on vortices in rotating superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ have been conducted in the Low Temperature Laboratory at Helsinki University of Technology during the past five years. These experiments have revealed unique vortex phenomena that are not observed in any other known superfluids. In this review, the concept of broken symmetry is applied to investigate the quantized vortex lines in superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. In the superfluid $A$ phase, vorticity can be supported by a continuous winding of the order parameter; this gives rise to continuous "coreless" vortices with two flow quanta. Novel vortices with a half-integer number of circulation quanta may also exist in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$ due to a combined symmetry of the superfluid state. In the superfluid $B$ phase, the vortices have a complicated core structure. The vortex-core matter is ferromagnetic and superfluid, and it displays broken parity. The ferromagnetism of the core is observed in NMR experiments due to a gyromagnetic effect. The calculated core structures exhibit an experimentally observed first-order phase transition. This vortex-core transition in rotating ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$B$ may be understood in terms of a change in the topology for flaring-out of the vortex singularity into higher dimensions; the topological identification further suggests that the phase transition manifests a spontaneous bifurcation of vorticity—involving half-quantum vortices in ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$B$. These recent advances of interest in quantum liquids are also of general relevance to a wide range of fields beyond low-temperature physics.

Neutrino-electron scattering experiments can elucidate the flavor content, spectrum shape, intensity, time dependence, and angular distribution of solar neutrinos. The author presents detailed calculations for all of the important solar neutrino sources of the predicted energy and angular dependence of the recoil electrons, as well as the total cross sections. In addition, the author discusses how neutrino-electron experiments can help distinguish between various proposed solutions of the solar neutrino problem.

The theoretical framework for describing the production of direct photons in hadronic collisions is reviewed. A detailed comparison between the theoretical predictions and existing data is presented along with a critical evaluation of the various sources of theoretical uncertainty. The information available from direct-photon experiments is contrasted with that learned from jet or single-hadron production. Prospects for new types of measurements in future experiments are also presented.

This work completes a two-part review on waves in gases, of which the first part [Rev. Mod. Phys. 58, 117 (1986)] dealt with the modern aspects of acoustics of jets, turbulence, and ducts; this second part extends the range of topics from sound to magnetic, internal, and (to a lesser extent) inertial waves, thus considering all four restoring forces (pressure, gravity, and Lorentz and Coriolis forces). The motivations for the study of these waves were outlined in the introduction to Part I. Part II reviews the coupling of acoustic, magnetic, and internal waves, in four stages: in Sec. I dispersion relations are used to study the propagation and radiation of magneto-acoustic-gravity-inertial waves in media for which the wave speeds and scattering scales are constant; in Sec. II the case of linear waves in stratified media, with nonuniform propagation velocity, is then discussed by means of special functions, appearing as exact solutions of second-order problems; in Sec. III the study of linear waves with variable propagation speeds is extended to certain classes of higher-order problems including a discussion of cutoff frequencies, critical levels, partition of energy, mode coupling and conversion, etc; in Sec. IV the preceding studies are extended to damped and nonlinear waves, to include dissipation with variable damping scales and large disturbances in media under nonuniform external forces, such as magnetic flux tubes. The conclusion (Sec. V) sums up both parts of the review, in the sense that it deals with all types of waves in fluids; it mentions a few currently controversial topics, points out some directions for future research, and indicates methods available to address these issues.

The authors discuss the concepts on which the interacting boson model is based, in particular those of pairing and seniority, which lead to a connection with the shell model. They review some of the calculations performed so far using these concepts and briefly comment on their results.

This review covers the progress in the study of vortex oscillations in rotating superfluids. The paper deals with the theory as its principal concern, but the experiments that one can compare with the theory considered are also discussed. Attention is focused mainly on the effects of crystalline order in the vortex lattice (the Tkachenko waves especially) and on the boundary problems arising in studies of vortex oscillations in finite containers. The approach is based mostly on the continuum hydrodynamic theory dealing with dense vortex arrays, and considerable attention is devoted to discussion of this theory in order to understand better the principles upon which the obtained results rest. The theory is traced from the simple description of a rotating classical fluid with continuous vorticity, through that of a perfect fluid with quantized vorticity in the form of an array of vortex lines, then the two-fluid theory of an isotropic superfluid, and finally the theory of rotating anisotropic superfluids such as ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-$A$. Applications of the theory to He II, the superfluid phases of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$, and the superfluid neutron matter in pulsars are discussed.

We trace the fundamental developments and events, in their intellectual as well as institutional settings, of the emergence of the quantum-mechanical electron theory of metals from 1928 to 1933. This paper continues an earlier study of the first phase of the development—from 1926 to 1928—devoted to finding the general quantum-mechanical framework. Solid state, by providing a large and ready number of concrete problems, functioned during the period treated here as a target of application for the recently developed quantum mechanics; a rush of interrelated successes by numerous theoretical physicists, including Bethe, Bloch, Heisenberg, Peierls, Landau, Slater, and Wilson, established in these years the network of concepts that structure the modern quantum theory of solids. We focus on three examples: band theory, magnetism, and superconductivity, the former two immediate successes of the quantum theory, the latter a persistent failure in this period. The history revolves in large part around the theoretical physics institutes of the Universities of Munich, under Sommerfeld, Leipzig under Heisenberg, and the Eidgenössische Technische Hochschule (ETH) in Zurich under Pauli. The year 1933 marked both a climax and a transition; as the laying of foundations reached a temporary conclusion, attention began to shift from general formulations to computation of the properties of particular solids.

Recent numerical Monte Carlo simulations of the hadron spectrum are reviewed. After a general introduction, different ways of calculating the hadron masses in the "quenched approximation" (i.e., neglecting virtual quark loops) are described and the latest results are summarized. The pseudofermion method and the iterative hopping expansion method for the introduction of dynamical quarks is discussed, and the first results for the hadron spectrum including the effect of virtual quark loops are reviewed. A separate section is devoted to the discussion of questions related to scaling with dynamical quarks.

This is a pedagogical review of some aspects of quantum field theories in the limit in which the number of internal degrees of freedom is large. The focus is on large-$N$ QCD. The authors briefly discuss several well-known approaches to a solution of the $N=\infty$ limit: loop equations, classical actions, and master fields. Eguchi-Kawai models are discussed in detail, and some recently obtained numerical results are reviewed.

The continuous operation of a tokamak fusion reactor requires, among other things, a means of providing continuously the toroidal current. Such operation is preferred to the conventional pulsed operation, where the plasma current is induced by a time-varying magnetic field. A variety of methods have been proposed to provide continuous current, including methods that utilize particle beams or radio-frequency waves in any of several frequency regimes. Currents as large as half a mega-amp have now been produced in the laboratory by such means, and experimentation in these techniques has now involved major tokamak facilities worldwide.