The problem of a spherically symmetric radiating body was first considered by Vaidya, who obtained what is often referred to as the "radiating Schwarzschild metric." It is well known that this metric, if expressed in radiation coordinates, differs from the Schwarzschild metric only in that the parameter $m$ has been replaced by a function of retarded time. In this paper, the parameter $m$ of the Kerr metric is considered to be a function of the retarded time and an exact expression for the energy tensor is obtained. It is shown that if $\frac{a}{m}$ is small then this energy tensor is appropriate for directed radiation. To this approximation [i.e., terms of order ${\left(\frac{a}{m}\right)}^2$ are neglected] the Landau-Lifschitz pseudotensor is used to show that the angular momentum radiated is $-m^{\prime }a$. The metric is also used to describe the physical properties of a slowly rotating radiating spherical shell, and it is shown that (provided $\frac{2m}{R}\ll 1$) the radiation gives rise to surface pressures pro-portional to the momentum radiated.

We show that all the minimum uncertainty packets are unitarily equivalent to the coherent states and that coherence is in fact stationary minimality.

An analysis of general scalar-tensor gravitation theory, containing two arbitrary functions of the scalar field, is presented. The weak-field limit is considered in detail, and predictions for the classical tests of gravitation theory are derived. A definite relationship between the light propagation and perihelion shift effects is found to hold under very general conditions. The theory of the detection of gravitational waves is also investigated, and the observable differences between the scalar and tensor components are indicated. Finally, the relationship between the properties of the source and its radiation is considered in the weak-source limit, and expressions for the rate of energy loss are derived. It is shown that the existing observational data are consistent with the possibility that the scalar field represents a major component of gravitational radiation from astronomical sources.

Some new quantitative tests of duality for elastic amplitudes at $t=0\mathrm{}$ are discussed.

The cross section for the production of the (hypothetical) intermediate vector boson of weak interactions ($W$ boson) in the reaction ${\nu }_{\mu }+p\to \mu +W+\Gamma$, where $\Gamma$ is a hadronic state unassociated with nucleon resonances, is calculated. The input to the numerical calculation is derived from analyzed results of the recent SLAC deep-inelastic $e-p$ scattering experiment. Owing to the mild momentum-transfer dependence of the observed $\gamma p\Gamma$ vertex, the resulting $W$-boson production cross section is found to be important only near threshold and to contribute a non-negligible amount to the total production cross section if the ratio of $W$-boson mass to nucleon mass is much larger than 1.

The calculations of a previous paper on Reggeized $U\left(6\right)\mathrm{}\otimes U\left(6\right)\mathrm{}\otimes O\left(3\right)\mathrm{}$ and absorptive correction cuts for ${\pi }^{-}p\to {\pi }^{0}n$ are extended to 70 GeV/c, an energy presently obtainable by the Serpukov accelerator.

It is shown that simple quark models with a current-current interaction do not lead to the results of the $\Delta I=\frac{1}{2}$ rule. Previous calculations giving these results effectively treat quarks as bosons.

The differential cross section and $\rho$ density-matrix elements for the reaction ${\pi }^{+}p\to {\rho }^0{\Delta }^{++}$ at 13.1 GeV/c are presented. The data are interpreted in terms of an absorption model with conventional pion exchange. The transverse ${\rho }^0$ production is compared with the predictions of vector dominance.

The effect of the mass difference between charged and neutral pions on the two-pion-exchange (TPE) phase parameters is studied by using the mass-averaging procedure of El-Ghabaty, Gupta, and Kaskas. It is found that the differences between the TPE parameters for isotriplet $p-p$ and $p-n$ scattering are generally less than 1%, while these differences for the one-pion-exchange phase parameters are known to be as large as 10%.

An additional Regge pole with a negative residue and a positive signature is suggested to fit the high-energy ${\pi }^{-}p$ total cross sections recently measured at Serpukhov. We give some experimental implications for the total cross sections and the ratio of the real to the imaginary part of the forward scattering amplitude of ${\pi }^{\pm }p$ at high energies.

With the availability of higher accelerator energies in the foreseeable future, it is to be expected that renewed efforts will be made to search for the hypothetical intermediate bosons in the next generation of neutrino experiments. We record here some details of the theoretical calculation of the production cross section upon which the numerical computation is based. The differential cross section is computed in closed form. The calculation of the total cross section is reduced to a two-dimensional integral to be evaluated numerically.

Dispersion relations and the hard-meson method of Schnitzer and Weinberg are used to study the radiative leptonic decay of the $K^{+}$. It is shown that in the pole-dominance approximation the relevant form factor in the axial-vector amplitude cannot be unsubtracted. Possible alterations of our results arising from relaxing a smoothness approximation are estimated to be small. We discuss and compare various symmetry-breaking schemes for the evaluation of necessary coupling constants. The branching ratio for $K^{+}\to \gamma e^{+}\nu$ is calculated to be ∼2.5×${10}^{-5\mathrm{}}$ for interesting structure-dependent decays. This is comparable to that for $K\to e\nu$ and two orders of magnitude larger than one would expect from the usual estimates for electromagnetic decays. The feasibility of experimentally observing the decay is discussed, as are the possible effects of electromagnetic violations of time-reversal invariance. From these results, a soft-pion estimate of $F_4$, the vector form factor in $K_{l4\mathrm{}}$, yields $\left|F_4\right|\approx 6.9$.

Using the closure approximation, we derive a simple relation between the total forward cross section for elastic scattering of neutrinos by nuclei and the corresponding total muon-capture rates. This relation is in good agreement with previous estimates of neutrino scattering cross sections, but still in disagreement with recent experimental data.

We propose a method for generating Regge cuts based on the multiperipheral model in the approximation of vanishing coupling of the Pomeranchuk trajectory to production processes. We utilize a formalism which explicitly satisfies the full unitarity equations, including inelastic terms, for all connected multiparticle production amplitudes as well as for the two-body amplitude. The sign of the Regge cut coincides with the sign of the cut in the absorptive model, and is opposite to that of the Amati-Fubini-Stanghellini cut. The results are applied to the recent Serpukhov $\mathrm{pp}$ data.

A simple interpretation is given to the diffraction model for electroproduction and photoproduction, on the basis of which we venture to provide answers to the question: When will electroproduction and photoproduction data show diffractive features? Conjectures are also made regarding the region of validity for Sakurai's results on electroproduction.

We discuss high-energy inelastic neutrino-nucleon processes in the light of recent theoretical and experimental developments for the corresponding electroproduction processes. We review the kinematics for the process in a form especially convenient for experimental analysis. We discuss sum rules and results related to current commutation relations. Consequences of the parton model and diffractive models are considered. Other results are: (1) The vector and axial-vector contributions to the total cross section are equal, provided the only symmetry-breaking term in the energy density transforms like a quark-mass term under $U\left(6\right)\mathrm{}\otimes U\left(6\right)\mathrm{}$. (2) Scale invariance of one of the three form factors ($\nu \beta$ or $\nu {\mathrm{W}}_2$) describing the process implies a neutrino total cross section which rises linearly with laboratory energy, provided the lepton current is local and there is no $W$ boson. The effect of a $W$ boson on this result is studied. (3) The relation of existing neutrino data and electroproduction data given by the conserved-vector-current hypothesis is studied and found compatible with experiment.

A simple model formula for the hadronic form factors as a ratio of two $\Gamma$ functions is examined from the point of view of its consistency with the beta-function model and with the chiral properties of the vector and axial-vector currents. It is shown that similar models may hold simultaneously for the simplest vector and axial-vector form factors while maintaining consistency with the Veneziano model of the four-point function, and with the requirements of a conserved vector current, partially conserved axial-vector current, and the Gell-Mann algebra of currents. An infinite class of such solutions is found: Defining form factors by $〈{\pi }^{+}\left(p_2\right)\left|{V_{\mu }}^0\mathrm{}\right(0\left)\right|{\pi }^{+}\left(p_1\right)〉=F_V\mathrm{}\left(t\right)\mathrm{}{(p_1+p_2)}_{\mu }$ and $〈\sigma \left(p_2\right)\left|{A_{\mu }}^0\mathrm{}\right(0\left)\right|{\pi }^0\left(p_1\right)〉={F_A}^{+}\mathrm{}\left(t\right)\mathrm{}{(p_1+p_2)}_{\mu }+{F_A}^{-}\mathrm{}\left(t\right)\mathrm{}{(p_1+p_2)}_{\mu }$, where $t={(p_1+p_2)}^2$, we find the solutions $F_V\mathrm{}\left(t\right)\mathrm{}\propto \frac{\Gamma (1-{\alpha }_V\mathrm{}(t\left)\right)}{\Gamma (r_V+1-{\alpha }_V\mathrm{}(t\left)\right)}$ and ${F_A}^{+}\mathrm{}\left(t\right)\mathrm{}\propto \frac{\Gamma (1-{\alpha }_A\mathrm{}(t\left)\right)}{\Gamma (r_A+1-{\alpha }_A\mathrm{}(t\left)\right)}$, where ${\alpha }_V\mathrm{}\left(t\right)\mathrm{}$ is the $\rho$ Regge trajectory and ${\alpha }_A\mathrm{}\left(t\right)\mathrm{}$ is the $\pi -A_1$ Regge trajectory. The power behaviors of $F_A\mathrm{}\left(t\right)\mathrm{}$ and $F_V\mathrm{}\left(t\right)\mathrm{}$ for $\mathrm{}\left|t\right|\mathrm{}\to \infty$ are not determined absolutely, but the relative power is found to be $r_V-r_A=\frac{1}{2}$, as a consequence of a quantization rule for the trajectory intercepts. Scalar and pseudoscalar form factors are treated also, with similar results; in the approximation used here, however, it is required that the pseudoscalar form factor $P\left(t\right)\mathrm{}$ in $〈\sigma \left(p_2\right)\left|{\partial }_{\mu }{A_{\mu }}^0\mathrm{}\right(0\left)\right|{\pi }^0\left(p_1\right)〉={M_{\pi }}^{2}P\left(t\right)\mathrm{}$ be dominated by the ground-state pion alone, that is, $P\left(t\right)\mathrm{}\propto \frac{\Gamma (-{\alpha }_A\mathrm{}(t\left)\right)}{\Gamma (1-{\alpha }_A\mathrm{}(t\left)\right)}$, in order to ensure absence of non-gauge-invariant terms in the matrix element $〈{\pi }^{+}\left(p_2\right)\left|{V_{\mu }}^0\mathrm{}\right(0\left)\right|{\pi }^{+}\left(p_1\right)〉$. In order to consider matrix elements of the vector- and axial-vector-current operators between other hadron states, we write generalized field-current identities, using the forms of $F_V\mathrm{}\left(t\right)\mathrm{}$ and ${F_A}^{+}\mathrm{}\left(t\right)\mathrm{}$, and make a universality hypothesis that the vector mesons $\rho$ and $A_1$ and their higher recurrences couple universally to the independent helicity amplitudes of the Breit frame. As an example, a treatment of the nucleon electromagnetic and axial-vector form factors is given, leading to simple model formulas for the Sachs form factors $G_E\mathrm{}\left(t\right)\mathrm{}$ and $G_M\mathrm{}\left(t\right)\mathrm{}$, and the axial-vector form factor $G_A\mathrm{}\left(t\right)\mathrm{}$, which for spacelike values of $t$ agree well with the experimental results.

The assumptions frequently made in current algebra together with Regge asymptotic behavior give a sum rule for ${W_3}^{\nu }(Q^2\approx 0, \nu )+{W_3}^{\overline{\nu }}(Q^2\approx 0, \nu )$ that involves only physically observable quantities.