Dawson-Oberman high-frequency long-wavelength conductivities of solid-state plasmas in thermal equilibrium are derived using a variational formalism. These derivations are different from those of other authors and give additional insight into the nature of the approximations implicit in their results. The final expressions reflect screened carrier-carrier and carrier-phonon interactions. They extend published conductivity formulas principally in their inclusion of deformation-potential phonon-carrier coupling.

A path-integral formulation of quantum mechanics is investigated which is closely related to that of Feynman. It differs from Feynman's formulation in that it involves the Hamiltonian function of the canonically conjugate coordinates and momenta. The classical limit yields the variational principle: $\delta ff(p‡-N)dt=0\mathrm{}$. A path-integral formula is also obtained for the energy eigenstate projection operator associated with the time-independent Schrödinger equation. The classical limit of the projection operator formula yields a modified form of the well-known variational principle for the phase-space orbit of given energy. Relativistically covariant Hamiltonian variational principles are analyzed and lead naturally to a relativistic scalar wave equation which involves a proper time variable which is canonically conjugate to the mass in the same manner as the ordinary time variable is conjugate to the energy in nonrelativistic quantum theory.

Few theories have generated so much emotion amongst physicists as the Regge Pole theory has ··· and still does. With the gradual accumulation of a vast amount of precise experimental data, it has become possible to attempt to give an objective survey of the present status of the theory in relation to experiment. The analysis herein is restricted to elastic and charge-exchange scattering processes in the region of high energies and small momentum transfers. A strong distinction is made between strictly forward ($t=0\mathrm{}$) and nonforward ($t\lesssim 0$) processes. In discussing the latter, an attempt is made to examine the phenomenological validity of the so called "factorisation theorem," the proof of which depends critically upon the assumption of the Regge poles being simple poles.

In this paper, we examine an argument of Jauch and Piron, which aims to prove the impossibility of hidden variables underlying the quantum theory, on the basis of certain assumptions that are weaker than those used by von Neumann for the same purpose. We show that, while the assumptions of Jauch and Piron are in fact weaker than those of von Neumann, the net result is that they actually prove nothing new at all. The conclusions of Jauch and Piron concerning the nonexistence of hidden variables are indeed seen to follow from a false assumption; i.e., that the impossibility of propositions that describe simultaneously the results of measurements of two noncommuting observables is an "empirical fact." Actually, it is shown that this assumption follows if and only if one first assumes what the authors set out to prove; i.e., that the current linguistic structure of quantum mechanics is the only one that can be used correctly to describe the empirical facts underlying the theory.

The measurement problem in quantum mechanics is re-examined and it is shown that it cannot really be solved in a satisfactory way, within the framework of the usual interpretation of the theory. We then discuss von Neumann's attempts to prove that quantum mechanics is incompatible with the introduction of hidden variables, and develop a more detailed form of Bell's argument, showing that von Neumann's analysis is invalid. Using certain ideas that are implicit in the "differential-space" theory of Wiener and Siegel, we go on to propose a new deterministic equation of motion, describing a kind of coupling of the measuring instrument to the observed system that explains in detail how the wave packet is "reduced" during a measurement in a continuous and causally determined way. By averaging over the hidden parameters, we then recover the usual statistical results of quantum mechanics as a special case. However, a more detailed analysis of the theory shows that new experimental and theoretical questions can now be raised, which go outside the framework of the quantum theory as it is now formulated. These questions are examined briefly.

The demonstrations of von Neumann and others, that quantum mechanics does not permit a hidden variable interpretation, are reconsidered. It is shown that their essential axioms are unreasonable. It is urged that in further examination of this problem an interesting axiom would be that mutually distant systems are independent of one another.

A survey of recent experimental and theoretical results (January 1963-July 1965) on fast-neutron-induced reactions is presented. The first part gives an outline of present reaction mechanism theories that may be useful for an experimentalist. A semiclassical and a more exact description of both direct and equilibrium processes is given and a brief discussion of intermediate processes included. The second part gives the experimental results relevant to the understanding of the mechanism of the interaction of neutrons with nuclei: energy spectra, angular distributions, and total cross sections. Finally, a survey is presented of the results and possibilities of utilising fast neutrons for nuclear structure investigations.

Available thermal diffusion data on He, Ne, Ar, Kr, Xe, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, CO, C${\mathrm{H}}_4$, N${\mathrm{H}}_3$, HCl of different workers have been discussed. This study has revealed the need and nature of the additional measurements which will be useful and is thus of help in planning new experiments. The problems of temperature assignment and composition dependence of the thermal diffusion factor ${\alpha }_T$ are examined. The adequacy of the theoretical ${\alpha }_T$ expression used while interpreting the experimental results is also given proper consideration. Comparison of the experimental data are made with the prediction of the regorous Chapman-Enskog kinetic theory in conjunction with the three spherically symmetric potentials (Lennard-Jones 12-6, modified Buckingham exp-6, and Morse) for nonpolar gases, while a Stockmayer type 12-6-3 potential for polar gases. Reasonably satisfactory agreement is obtained even for polyatomic gases. The extent to which Chapman-Enskog theory in conjucntion with central force-field models may be expected to hold for polyatomic gases is investigated The up-to-date knowledge of the kinetic theory which takes into consideration inelastic molecular collisions is reviewed

Our previous treatment of noise in the nonequilibrium steady state is extended to include nonstationary processes, and processes for which the quasilinear approximation is inadequate. By use of backward-equation methods, we show that $M_0(a_0, t, t_0)=〈〉\left(\exp \left[-\int {t_0}^{t}Q\left(a\right(s), t-s) \mathrm{ds}\right]\right)$ subject to $\mathrm{a}\left(t_0\right)={\mathrm{a}}_0$ obeys the differential (integral) equation: $\frac{\partial M_0(a_0, t, t_0)}{\partial t_0}=\left[Q\right(a_0, t-t_0)-\Sigma \stackrel{\infty }{n=1\mathrm{}}{\mathrm{D}}_n(a_0, t_0):{\left(\frac{\partial }{\partial a_0}\right)}^n]M_0,$ where the ${\mathrm{D}}_n$ are the $n\mathrm{th}$-order diffusion coefficients of the $\mathrm{a}\mathrm{}\left(s\right)\mathrm{}$ process, and $Q\left(\mathrm{a}\mathrm{}\right(s), s)$ is an arbitrary function of a and $s$. The choice $D_n=0\mathrm{}$, $n>\mathrm{}2\mathrm{}$, $D_2=D$ $D_1\mathrm{}\left(a\right)=-\Lambda a$ makes $a\left(s\right)\mathrm{}$ an Ornstein-Uhlenbeck (O.U.) process, i.e., white noise that has been filtered through an $\mathrm{RC}$ network with time constant $\frac{1}{\Lambda }$. The choice $Q\left(a\right(s), s)=k(t-s)\mathrm{}{\mathrm{}\left[a\right(s\left)\right]}^2$ squares the output and applies the time smoothing $k(t-s)\mathrm{}$. For $k\left(s\right)=\exp (-2\mathrm{}\beta s)$ [time smoothing through an $\mathrm{RC}$ network with time constant $\left(\frac{1}{2\beta }\right)$], an explicit solution is obtained for the characteristic function $M_0$. For arbitrary positive $k\left(s\right)\mathrm{}$, we show that $M_0$ becomes independent of $a_0$ as $t\to \infty$ if $k\left(\infty \right)=0\mathrm{}$, and $M_0$ becomes stationary if $\Lambda >0\mathrm{}$ and $\int 0^{\infty }k\left(u\right)\mathrm{} \mathrm{du}<\mathrm{}\infty .$

A previous work dealing with bound states in a Coulomb potential is extended to the case of scattering states. The symmetry of the problem under the Lorentz group 0(1,3) is used to construct wave functions. Harmonic analysis on two-sheeted hyperboloids is briefly discussed in arbitrary dimension. The set of scattering states for both an attractive and a repulsive potential is shown to provide a unitary representation of the group 0(1, 4).

The internal 0(4) symmetry group of the nonrelativistic hydrogen atom is discussed and used to relate the various approaches to the bound-state problems. A more general group 0(1,4) of transformations is shown to connect the various levels, which appear as basis vectors for a continuous set of unitary representations of this noncompact group.

In this article we review the calculations and experimental information available in the studies of electron scattering (elastic and inelastic) from the magnetic-moment distribution of nuclei. The corresponding information on the properties of nucleons has been reviewed previously and is not discussed here. As usual in electron-scattering investigations we are concerned mostly with the determination of two functions of the momentum transfer, the charge and magnetic form factors or linear combinations of them, which are closely related to the spatial structure of the charge and magnetic-moment distributions. We specialize the discussion to the magnetic form factor and the nuclear properties connected with it.

First, we show that the most important equations of the dynamics of the two types of superfluids, He ii and superconductors, follow quite directly from the simple assumption that the quantum field of the particles has a mean value which may be treated as a macroscopic variable. The background of this ansatz is also discussed. Second, we apply these equations to various physical situations in He ii, notably the orifice geometry and the superfluid film, and show how they, and particularly the idea of phase slippage accompanying all dissipative processes, can be applied and what kinds of macroscopic interference phenomena may be expected. The effect of synchronization in the ac interference experiment is discussed.

Emphasis in this review of current problems in the study of the interstellar medium is on a few specialized topics. The first treated is the problem of the cloud structures and the velocity fields in the interstellar gas. Another section deals with the observations suggesting the presence of dust as well as gas in the medium and with the proposed nature of the dust grains. These grains were the first indicators of the presence of a general galactic magnetic field and are believed to be catalytic agents in the formation of molecules in the gas. The status of current observational investigations of the magnetic field and of current theoretical studies of the formation of interstellar molecules is described. Finally, very recent observations in the microwave spectrum of the hydroxyl radical are outlined. These suggest the availability of new and surprising information about conditions in the interstellar medium.

A review is given of recent applications of symmetry arguments in particle physics. It deals with the developments which start with $\mathrm{SU}\left(6\right)\mathrm{}$.

An elementary account is given of the representation theory for unitary groups. We review the basic definitions and the construction of irreducible representations using tensor methods, and indicate the connection to the infinitesimal approach. Special attention has been given to the detailed procedure to obtain Clebsch-Gordan series and to the problem of finding the ($S{U}_m, S{U}_n$) content of an irreducible representation of $S{U}_{\mathrm{mn}}$ or $S{U}_{m+n}$. An appendix summarizes the properties of the Young operators used in constructing the tensor representations; this provides the link with the representation theory of the symmetric groups. We include a tabulation of various decompositions which appear in the text and of Weyl's dimension formula for tensor representation.

A survey of the experimental data for $E1\mathrm{}$ transitions between levels below nucleon emission threshold in medium and heavy nuclei is presented. A general classification of these transitions is proposed and it is shown that, within most of the classes defined, the experimental "reduced" $E1\mathrm{}$ transition probabilities differ by less than a factor ${10}^4$. The data are compared with specific nuclear model predictions. Precise theoretical descriptions of the anomalous parity states involved in $E1\mathrm{}$ transitions exist in a few cases only. However it is often possible to link the observed behavior of $E1\mathrm{}$ transition rates as a function of different parameters, with qualitative model predictions.

The data available before 1 January 1965 are presented in tables including level lifetimes, quantum numbers, branching rati s, internal-conversion data, and deduced transition probabilities.

By introducing complex canonical coordinates, classical and quantum mechanics may be embedded in the same formulation. In such a way, the connection between Poisson brackets and commutators, canonical transformations and unitary transformations, etc., become apparent. This formulation is also particularly suitable for discussing the classical limit of quantum mechanics and for quantum-statistical mechanics.

The spectral distribution of light scattered by density fluctuations in a dense, monatomic, one-component fluid is calculated from the time dependence of the density fluctuations predicted by the linearized hydrodynamic equations of irreversible thermodynamics. The results of Landau and Placzek are verified and a procedure for deriving correction terms is discussed with the dispersion in the velocity of thermal sound waves obtained as an illustration. Particular attention is paid to the critical region. The properties of carbon dioxide are used to estimate the spectral distribution of critical opalescence. A comparison is made between light-scattering and sound-propagation experiments. Space dispersion near the critical point in the pressure and the thermal conductivity is examined briefly. Finally, some of the experimental problems involved in measuring the spectral distribution of the scattered light are discussed.

A study is made of the effect of temperature and environment on the absorption spectra of simple systems. In part I the longitudinal and transverse susceptibilities of a two-level system are analyzed in terms of simple stochastic models. Particular attention is paid to the different roles played by the phase-interruption and frequency-modulation mechanisms. A calculation is given of the susceptibility of a harmonic oscillator perturbed by interaction with other oscillators. In part II the same systems are studied using Green's function methods. It is assumed that the two-level system is coupled to a crystal lattice by an isotropic interaction that is linear in the lattice displacement. Expressions are obtained for the longitudinal and transverse susceptibilities and comparison is made with the results of part I. The susceptibility of the harmonic oscillator is calculated and found to be identical to the susceptibility obtained by more elementary methods.