Some remarks are made about the recoil deuteron vector polarization in elastic electron-deuteron scattering and the relation to time-reversal invariance.

We show the general features to be expected in scattering at energies high enough that the scattering amplitude consists of only the Pomeranchuk Regge pole and the two-Pomeranchuk-cut terms. The predictions of the Reggeized multiple-scattering quark model for pion-nucleon scattering at lab momenta up to $500\frac{\mathrm{GeV}}{c}$ are given as a specific example.

Using appropriate continuity arguments in the ${\mathrm{SU}}^{\mathrm{}(+)\mathrm{}}\mathrm{}\left(3\right)\mathrm{}\otimes {\mathrm{SU}}^{\mathrm{}(-)\mathrm{}}\mathrm{}\left(3\right)\mathrm{}$ subgroup space, a new sum rule has been derived for $K_{l3\mathrm{}}$ decays. This sum rule incorporates corrections to the soft-pion theorem and contains $K_{l3\mathrm{}}$ form factors defined at a point much closer to the physical decay region.

The role of the $Z^{*}$'s is discussed on the basis that the badly broken nonchiral $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$ internal symmetry is also relevant for the classification of hadronic states, complementing the well-established broken $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry. If we assume that the $Z^{*}$'s belong to (½,½) representation of $\mathrm{SU}\left(2\right)\mathrm{}\times \mathrm{SU}\left(2\right)\mathrm{}$, we can expect one or more sets of $Z_0^{}{}_{}{}^{*}$ and $Z_1^{}{}_{}{}^{*}$. Each ($Z_0^{}{}_{}{}^{*},Z_1^{}{}_{}{}^{*}$) set is nearly mass degenerate and has the same spin and parity.

We have examined, by an approximate method, the electromagnetic radiative corrections at high energy to the lowest-order weak amplitudes ${\nu }_{\mu }+{\overline{\nu }}_e\to {\mu }^{-}+e^{+} \mathrm{and} {\nu }_{\mu }+e^{-}\to {\mu }^{-}+{\nu }_e$.

Assuming the anomalous axial-vector Ward identity for the $〈\mathrm{VVA}〉$ three-point functions, we calculate the $\rho -\omega -\pi$ and $\rho -\varphi -\pi$ vertex functions and the off-mass-shell ${\pi }^0\gamma \gamma$ form factor in the framework of Schnitzer and Weinberg's hard-meson calculations. The mass-shell value of the form factor reduces to a result of Adler; and its off-mass-shell values are used to predict certain electron-positron annihilation cross sections. We compare the results of the present model with those of the conventional vector-meson-dominance model.

The relationship between Regge cuts and absorption is reviewed. A detailed numerical study is carried through for the Gottfried-Jackson absorption model as applied to the reaction $\gamma p\to {\pi }^{0}p$ with Reggeized $\omega$ exchange. The absorption parameters are set from $\pi p$ elastic scattering data. Calculations of $s$- and $t$-channel amplitudes and cut discontinuities are presented and discussed as regards their advantages and shortcomings for fitting the neutral-pion photoproduction data. Several published fits are compared. We conclude that the cut contribution must be roughly doubled to obtain a successful fit.

Several applications of a simple approach to unitarization in the case of the three-point functions of hard-meson theory are made. For the first of these, effective-range formulas are obtained for the pion form factor in the timelike region for both hard-pion current-algebra ($\delta =-\frac{1}{2}$) and Veneziano models. Next, the extension of this procedure to the case of several coupled channels is used to obtain an effective-range formula for the pion form factor which includes the small effect of the closed $K\overline{K}$ channel. Finally, an expression for the pion form factor is derived which allows for the inclusion of some nonresonant $p$-wave ($I=1\mathrm{}$) $\pi \pi$ scattering. Since this component is parametrized via the introduction of an additional (nonresonant) $p$-wave scattering length, the resulting expression for the pion form factor generates a one-parameter family of fits to the experimental data. The data appear to be consistent with a small positive nonresonant scattering length and favor a value of ${\Gamma }_{\rho }$ slightly less than 124 MeV.

A derivation is given in terms of the eikonal formalism of a recently derived upper bound on the absorptive part of a spin-zero elastic scattering amplitude. The multivaluedness inherent in the problem is explored, and considerably smaller upper bounds are obtained by imposing conditions of reasonability on the profile function. Experimental differential cross sections for ${\pi }^{\pm }p$ and $\mathrm{pp}$ elastic scattering over a wide energy range are found to fall on a universal curve, which lies just below our most stringent upper bound over a range of three decades in $\frac{d\sigma }{\mathrm{dt}}$.

A study of the possibility of using an absorption model to obtain a unique $s$-wave $I=0\mathrm{}$ $\pi \pi$ phase shift from the reaction ${\pi }^{-}p\to {\pi }^{-}{\pi }^{+}n$ was made. Applying the model to combined data from several latoratories, we obtained a set of reasonable (but twofold ambiguous) values for the isospin-zero $s$-wave phase shift ${{\delta }_0}^0$, using the isotropic moment of the dipion decay distribution. Values for ${{\delta }_0}^0$ deduced by using the $s-p$ wave interference term in the dipion decay cross section agreed well with previous (twofold ambiguous) results obtained by extrapolation procedures. Comparing the two sets of twofold ambiguous solutions for ${{\delta }_0}^0$, the lower or "down" branch was preferred marginally in the dipion mass region below the $\rho$ meson. No unique conclusion could be drawn in the higher-mass region. We emphasize the model dependence of these results, but we believe that similar studies with improved statistics for $-t>\mathrm{}{\mu }^2$ would yield similar results. Good data for $-t<\mathrm{}{\mu }^2$ are required to do definitive model-independent analyses.

Commutators of the type $[{\dot{J}}_i,J_i]$, where $J_{\mu }$ is a vector or an axial-vector current, are expressed in terms of canonical $2^{+}$ meson fields. (More generally, a commutator involving the $n$th time derivative is expressed in terms of fields of spin $n+1\mathrm{}$.) One consequence is that electromagnetic mass differences are finite. Predictions are made for electroproduction and neutrino-induced production; where comparisons are possible, the agreement with experiment is excellent.

We have evaluated a contact interaction between the protons using the vector currents and wave functions provided by the relativistic $O(4,2)\mathrm{}$ model. The resulting enveloping differential cross section at $s=\infty$ is discussed and compared with experiment over the entire range of accessible momentum-transfer values.

A new and simpler technique is used to derive low-energy theorems on $K_{l3\mathrm{}}$ decay form factors $f_{+}\mathrm{}\left(0\right)\mathrm{}$ and $f_{-}\mathrm{}\left(0\right)\mathrm{}$ based on $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ symmetry breaking. We employ the $(3^{*},3)\oplus (3,3^{*})$ symmetry-breaking model for definiteness. Assumptions like field algebra, vector dominance, $c$-number Schwinger terms, or pole saturation are not used. The method yields the results of Callan and Treiman, Glashow and Weinberg, and Gerstein and Schnitzer in appropriate limits. The assumption under which our results agree with those of Dashen and Weinstein are also discussed. The sensitivity of the parameter $\xi \equiv \frac{f_{-}\mathrm{}\left(0\right)\mathrm{}}{f_{+}\mathrm{}\left(0\right)\mathrm{}}$ to assumptions of explicit symmetry breaking is demonstrated, and several conclusions are drawn.

The Reggeized absorptive cut is included in three Regge-pole (the $\Delta$, $N_{\alpha }$, $N_{\gamma }$) fits to backward $\pi N\to N\pi$ differential cross sections. The over-all framework of the Veneziano model is used, and successful fits are found with smooth one-parameter residues. The cuts remove the Veneziano model's contradictions with experiment, are essentially parameterless, and are definitely non-negligible. We discuss methods to verify their presence. The usual difficulty in extrapolating to the $\Delta$ mass (too small a width) remains unresolved. Possible explanations of this problem are discussed.

The complete gauge-invariant matrix element for the decays ${\overline{K}}^0\to {\pi }^{+}{l}^{-}\overline{\nu }\gamma$ ($l=e$ or $\mu$) is derived using the soft-photon theorems of Low and of Adler and Dothan. These theorems, along with several corollaries of them, are reviewed in detail and their application demonstrated by reference to the radiative $\overline{K}_{l3\mathrm{}}^{}{}_{}{}^0$ decay mode. The square of the matrix element is calculated using the theorem of Burnett and Kroll, and is compared with the result of a direct computer evaluation of the appropriate traces. Structure-dependent terms are discussed, and the dominant terms among those linear in the photon energy are estimated in the softpion and kaon limits. Results for the radiative photon spectra are given, together with the decay rates for a specific value of the minimum photon energy $E_0$.

The departure from $T$ invariance in neutral $K$-meson decays is shown to be directly demonstrable through suitable measurements. The predicted asymmetries include a $\mathrm{CP}$- and $T$-noninvariant effect larger than any which has been measured so far.

The dispersive sum-rule method, originally developed by Fubini and Furlan, is applied to $\pi -K$ elastic scattering. Sum rules are derived for the $I=\frac{1}{2}$ and $I=\frac{3}{2}$ scattering amplitudes, and the isospin-antisymmetric combination of the $s$-wave scattering lengths is calculated. These expressions contain terms involving the off-mass-shell kappa-kaon-pion coupling constant. By following a procedure introduced by Dashen and Weinstein, and assuming that the $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ symmetry-breaking part of the strong-interaction Hamiltonian transforms according to the $(3,3^{*})+(3^{*},3)$ representation of $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$, we evaluate the off-shell corrections. In the evaluation of the off-shell corrections, we obtain expressions for the postulated $\kappa$-meson mass and decay width, consistent with a recent experimental indication. The $s$-wave scattering lengths are consistent with other current-algebra and phenomenological-Lagrangian calculations, but smaller than those recently reported from calculations based on the leading term Veneziano model.

The recent Serpukhov data for $K^{-}p$ and earlier data for $K^{+}p$ collisions appear to contradict the Pomeranchuck theorem on the asymptotic equality of particle-target and antiparticle-target total cross sections. Experimental and theoretical consequences of the invalidity of the Pomeranchuk theorem are discussed. These include the result that forward amplitudes for $K^{-}p$ and $K^{+}p$ become asymptotically real.

Forward dispersion relations are used as the basis of an analysis of the information on pion-pion scattering available up to 850 MeV. These are shown to result in a model-independent relation between the scattering lengths ${\alpha }_0$ and ${\alpha }_2$, valid for all possible behaviors of ${{\delta }_0}^0$ in the $\rho$-region, and taking the value $\frac{a_0}{a_2}=-3.2\mathrm{}\pm 1.0$ from recent low-energy work, the values $a_0=0.16\mathrm{}\pm 0.04$, $a_2=-0.05\mathrm{}\pm 0.01$ uniquely result. The ambiguity in ${{\delta }_0}^0$ in the $\rho$ region is also studied, by four different methods, and uniquely resolved, allowing a detailed picture of all the phases up to 850 MeV to be given.

Assuming that the off-shell Ball amplitudes for ${\pi }^{-}+p\to {\rho }^0+n$ not only satisfy the constraints imposed by current conservation but also are smooth in the vector-meson mass, we predict all the amplitudes (including longitudinal) for ${\pi }^{-}+p\to {\rho }^0+n$ from single-pion photoproduction. Our model has no adjustable parameter, yet the calculated cross sections and density matrix are in reasonable agreement with experiment.