We demonstrate that much of the variation in mass shape and position of the $A_2\mathrm{}\left(1300\right)\mathrm{}$ meson from experiment to experiment is consistent with a model of two coupled or interfering wide- and narrow-width particles which may be close to forming a double-pole system. We find that the double-pole limit of this model leads to reasonably good fits for the mass spectra of the $\pi \rho$ and $K\overline{K}$ decay channels produced in ${\pi }^{-}p$ and $\overline{p}p$ collisions. Also, the model is consistent within experimental resolution with the available $\pi \rho$-decay channel mass spectra found in the reaction $K^{-}n\to {A_2}^{-}\Lambda$. Predictions for other reactions involving $A_2$ production are made.

Using the model-dependent assumption of $2\pi$ saturation of the unitarity sum, we find estimates for $\left|\frac{{\eta }_{00}}{{\eta }_{+-}}\right|$ and $\frac{\mathrm{Re}\epsilon }{\left|{\eta }_{+-}\right|}$ for a certain class of theories. Two models are tested, and $\left|\frac{{\eta }_{00}}{{\eta }_{+-}}\right|$ is found to be different from the originally estimated value, which was based on $\mathrm{Re}\epsilon$ as input.

The nucleon-nucleon phase shifts are calculated by adding the exchange of the scalar-isoscalar meson $\epsilon$ to our previous calculations based on the universal theory of primary interactions proposed by Sudarshan. Some improvements are obtained. In particular, the $1S_0$, $1D_2$, and $3P_2$ results are good for $\frac{g_{\epsilon N{N}^2}}{4\pi }=13.5\mathrm{}$ and a hard-core cutoff at 0.4 F.

The sign of the observed circular polarization of $\gamma$ rays emitted by nuclei is used to show that, in the Cabibbo theory of the weak interaction, the induced pseudotensor form factor of the axial-vector current satisfies the inequality $-2<\frac{f_T\mathrm{}\left(0\right)\mathrm{}}{f_A\mathrm{}\left(0\right)\mathrm{}}$.

An upper bound for the branching ratio for the decay $K^{\pm }\to {\pi }^{\pm }\nu \overline{\nu }$ is estimated in the conventional theory with no neutral currents.

Weinberg's first sum rule is coupled to a general isospin-conserving symmetry-breaking interaction to predict the $\omega -\varphi$ mixing angle along with associated vector-meson mass sum rules which are listed for comparison with experiment. Both ${\mathrm{}\left(\mathrm{mass}\right)\mathrm{}}^2$ and ${\mathrm{}\left(\mathrm{mass}\right)\mathrm{}}^{-2\mathrm{}}$ sum rules are considered.

In order to estimate the usefulness of Goldhaber-distribution analysis as a spin-parity text for four-pion resonances, the distributions for two spin-parity choices in each of two symmetry types are compared. The significance of two plotting schemes is investigated and the dependence of the results on the algebraic form assumed for the matrix element is estimated. Both plotting schemes are found to be useful and three of the four distribution types are relatively form-independent.

We have analyzed four interference models which can be constructed from Regge, resonance, and absorptive basic amplitudes. The models result from the hypothesis that the $S$ matrix factors into components which describe the contributions of various mechanisms (Regge, resonance, absorption) to the scattering. Additional terms, which involve integrals over products of the basic amplitudes, are thereby introduced naturally into the $T$ matrix for each model. This formalism takes account, at least in part, of the requirements of unitarity. Although the additional terms so introduced into the total amplitude eliminate much of the double counting present in, for example, the usual Regge-resonance model, the particular model constructed from resonance and absorption amplitudes gives the best agreement with experiments for $s\lesssim 5$ Ge${\mathrm{V}}^2$ even without any attempt at fitting. We then extend this model to higher energies by introducing Regge trajectories to support the recurrences of the low-lying $N$ and $\Delta$ resonances. After fixing the parameters of the trajectories by fitting the data up to $s=10\mathrm{}$ Ge${\mathrm{V}}^2$, we find that we obtain a good representation of the experimental data up to $s\approx 25$ Ge${\mathrm{V}}^2$. Our results lend additional support to the idea of duality, and suggest that several not well-established, as well as many new, resonances are needed to fit the data and do not require an isotopic spin-dependent absorptive amplitude.

A gauge-invariant one-vector-meson-exchange (OVE) model is constructed for the process $\gamma +N\to {\rho }^{\pm }+\Delta$. The form of the model is obtained by selecting the simplest extension of the OVE diagram consistent with gauge invariance. The $\Delta \rho N$-coupling strength is considered and discussed in terms of vector-meson dominance. It is found that the interference between the OVE and one-pion-exchange amplitudes vanishes.

Elastic unitarity is used to connect the pion electromagnetic form factor to the $\pi \pi$ Veneziano amplitude. A model for the form factor exhibiting this connection is obtained. It is in fair agreement with experiment.

The $\mathrm{QQ}\overline{Q}$ model proposed by Mitra is extended to incorporate the photoproduction processes $\gamma B\to \mathrm{PB}$, $\gamma B\to P{B}^{*}$, $\gamma B\to \mathrm{VB}$, and $\gamma B\to V{B}^{*}$ through a formulation of the basic mechanisms $\mathrm{VQ}\to \mathrm{VQ}$ and $\mathrm{VQ}\to \mathrm{PQ}$, where $P$ and $V$ denote the pseudoscalar and vector mesons, and $B$ and $B^{*}$ denote the octet and decuplet baryons, respectively. The consequences of this model are then investigated through the cross-section sum rules for various processes and the density-matrix analysis of the photoproduced $B^{*}$ or $V$. Clean geometrical results are obtained for the density matrices of $B^{*}$ for the processes of the type $\gamma B\to P{B}^{*}$ in the forward direction; these results agree well with the recent experimental data. A prediction for the corresponding angular distributions is also presented under the assumption of dominance of (-) amplitudes, which represent the transitions between the negative-parity $\mathrm{QQ}\overline{Q}$ states. For all processes of the type $\gamma B\to \mathrm{VB}$, we obtain for any angle $\phi$, ${{\rho }_{1-1}}^V=0\mathrm{}$. Angular distributions of the other density-matrix elements of the vector mesons for such processes are obtained under the following assumptions: (i) $Q\overline{Q}$ forces are spin- and unitary-spin-independent and operate mainly through the $s$ wave, and (ii) production processes are dominated by the (-) amplitudes. The agreement with experiment is again fairly good. A sum rule of the form ${{\rho }_{00}}^V=\left(\frac{8}{3}\right){{\rho }_{33}}^D$ is obtained in the forward direction relating the density matrix of the vector meson with that of the decuplet baryon for all processes of the type $\gamma B\to V{B}^{*}$. Cross-section sum rules for various processes are also presented and compared with experiment.

An expression is derived for a $K_{l4\mathrm{}}$ form factor correct to first order in chiral-symmetry breaking. The corrections seem to be of the correct sign.

A simple form of the pion electromagnetic form factor $F\left(s\right)\mathrm{}$ in a Veneziano-type representation is investigated. The derivation of this form factor makes use of Martin's $\mu$ plane in which the four-point Veneziano amplitude is represented by a single moving pole. The pion form factor thus obtained contains only one parameter. Using only unitarity near the threshold, this parameter can be determined. The result is $F\left(s\right)\mathrm{}\sim s^{-1.5\mathrm{}}$ in the spacelike region and ${\mathrm{}\left|F\right(s\left)\right|}^2\simeq 59$ at $s\approx {m_{\rho }}^2$, in reasonable agreement with the experimental data. Finally, the hypothesis that the Pauli-Dirac isovector form factor of the nucleon may be identified with the pion form factor is checked. The agreement with data is good.

By using quark-algebra equal-time commutation relations and a smooth pole-dominated form for the vector-vector-axial-vector vertex in the high-energy limit, one can describe the radiative decays of the vector mesons and the $\omega \to 3\pi$ decay in excellent agreement with experimental data. It is shown, however, that if we exploit all equations this procedure gives, we get into contradictions. By introducing a non-smooth amplitude, the contradictions can be eliminated in such a way that the good predictions of the smooth case remain unaltered. The various aspects of the results are discussed.

The differential decay rate for the double Dalitz decay ${\pi }^0\to e^{+}{e}^{-}{e}^{+}{e}^{-}$ is calculated exactly as a function of the virtual photon masses, with arbitrary form factors at the ${\pi }^0\to 2\gamma$ vertex. The result is compared with the result of an approximate calculation using only a single Feynman diagram.

It is shown in conventional Regge theory that the spin-density matrix elements of $\rho$ mesons produced by scattering pions off nucleons have the properties that $\frac{({\rho }_{11}-{\rho }_{1,-1})}{{\rho }_{00}}$ and $2{\left(\frac{\left|{\rho }_{10}\right|}{{\rho }_{00}}\right)}^2$ are equal and dependent only on pion exchange at very high energies. The ratio $\frac{{\rho }_{10}}{{\rho }_{00}}\simeq \frac{\left(\mathrm{Re}{\rho }_{10}\right)}{{\rho }_{00}}$ in a generalized Veneziano model is then found to agree with data at 8-GeV/c pion laboratory momentum.

The Faddeev equations are solved by means of Padé approximants. As an application of the method, the doublet and quartet scattering lengths of neutron-deuteron scattering are calculated for the case that the nucleon-nucleon interactions are described by central local Yukawa potentials.

The final-state interaction effects in the reaction ${\pi }^{-}+p\to {\pi }^{-}+K^0+{\Sigma }^{+}$ are analyzed in a perturbation model. It is shown that with a reasonably assumed $\pi -K$ interaction strength, some effects in the Dalitz plot can be produced. The $\pi -K$ rescattering effects on the polarization of the $\Sigma$ are examined. It is concluded that even if the rescattering effects are important, a determination of the parity of the ${Y_0}^{*}\mathrm{}\left(1405\right)\mathrm{}$ by measuring the polarization of the $\Sigma$ is still plausible.

The unitary Padé approximants, successfully introduced in strong-interaction physics for the pion and kaon systems, are now applied to the nucleon-nucleon problem. It is assumed that the interaction between two nucleons is described by the renormalizable Lagrangian $L_I=ig\overline{\psi }{\gamma }_5\tau \psi \Phi +\lambda {\left(\Phi ·\Phi \right)}^2$. We present the result of the complete calculation of the [1,1] unitary Padé approximant, which does not involve the second term in the Lagrangian: This implies that no free parameters appear in our model. A complete description of low-energy nucleon-nucleon physics is then obtained which qualitatively and often quantitatively agrees with experiment. Bound states appear only in $S$ waves, and a real pole is found in the deuteron amplitude at 4.8 MeV when the pion-nucleon coupling constant is taken at its physical value $\frac{g^2}{4\pi }=14.7\mathrm{}$. The Regge trajectories rise with energy: The deuteron recurrence does not become physical, while the recurrences of the virtual ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state give rise to narrow resonances in the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}G_4^{}{}_{}{}^{}$ waves. For all waves (with the exception of the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ which in the [1,1] Padé approximation has a wrong threshold behavior), the calculated phase shifts are in good qualitative agreement with the experimental phase-shift analysis.