The SLAC 2.2-m streamer chamber has been used to study photoproduction from hydrogen with a 16-GeV bremsstrahlung beam. The use of a single-hadron trigger permitted a study from 2 to 16 GeV which included photoproduction of the ${\Delta }^{++}$ and of the vector mesons $\rho$, $\omega$, and $\phi$. The sample reported here represents 87 000 pictures containing 7055 hadronic events of which about 2500 were above 5 GeV. Interesting aspects of the data are the dominance of ${\rho }^0$ production in the three-prong topology at high energies, the diffraction character of high-energy ${\rho }^0$ production, the clear indication of the transversality of the ${\rho }^0$ spin orientation, and the apparent interference between the resonant ${\pi }^{+}{\pi }^{-}$ (${\rho }^0$) production and a nonresonant background. Tests of the vector-dominance model are described, including a comparison of total photo-production cross sections derived from our data with those obtained elsewhere by direct measurements.

We have analyzed approximately 9000 four-prong events produced by ${\pi }^{-}p$ interactions at 6.7 GeV/c. All the effective-mass distributions from final states ${\pi }^{-}{\pi }^{-}{\pi }^{+}p$, ${\pi }^{-}{\pi }^{-}{\pi }^{+}{\pi }^{0}p$, and ${\pi }^{-}{\pi }^{-}{\pi }^{+}{\pi }^{+}n$ are presented, as well as cross sections. Resonances in each final state amount to more than 50% of total events, dominated by $\rho$ mesons and $\Delta \mathrm{}\left(1236\right)\mathrm{}$ baryons. Three-pion mass distributions show strong signals in the $A$-meson region in all three final states, but only a modest enhancement is observed in the $R$-meson region. We rule out $J^P$ of $0^{-}$ and $2^{+}$ for the $A_{1.5}$. A similar analysis for the $A_1$ is consistent with $1^{+}$. In the $\pi \rho$ and $\pi \eta$ mass distributions no evidence for $A_2$ structure is seen. Low-mass enhancements in four-pion mass distributions appear in the region of the $B$ meson and the $\rho \mathrm{}\left(1700\right)\mathrm{}$ meson. There is also possibly some evidence for $f^{\prime }\to 4\pi$. Higher-mass nucleon isobars are found to be closely associated with $\Delta \mathrm{}\left(1236\right)\mathrm{}$ production. There is no significant production of quasi-two-body final states.

An experiment has been carried out to search for uncharged particles with spacelike four-momentum which presumably travel faster than light. No evidence for such particles has been found. The results can be expressed as upper limits on the production rates for such particles by stopped $K^{-}$ and $\overline{p}$ compared to production rates of pions in similar reactions: $\frac{(K^{-}+p\to {\Lambda }^0+t^0)}{(K^{-}+p\to {\Lambda }^0+{\pi }^0)}\le 2\times {10}^{-3\mathrm{}}$, $\frac{(K^{-}+p\to {\Lambda }^0+t^0+{\overline{t}}^0)}{(K^{-}+p\to {\Lambda }^0+{\pi }^0)}\le 2.5\times {10}^{-3\mathrm{}}$, $\frac{(\overline{p}+p\to {\pi }^{+}+{\pi }^{-}+t^0)}{(\overline{p}+p\to 3\pi )}\le 2\times {10}^{-3\mathrm{}}$, $\frac{(\overline{p}+p\to {\pi }^{+}+{\pi }^{-}+t^0+{\overline{t}}^0)}{(\overline{p}+p\to 4\pi )}\le 1\times {10}^{-3\mathrm{}}$. Other sources of information placing limits on the interactions of tachyons are discussed.

The polarization and the differential cross section in ${\pi }^{-}p$ elastic scattering have been measured at incident pion laboratory momenta of 1.70, 1.88, 2.07, 2.27, and 2.50 GeV/c. The experiment was carried out at the Argonne zero-gradient synchrotron with a polarized proton target. Details of the apparatus and data analysis are presented here together with the final results. A partial-wave analysis of the data has verified the $J^P=\frac{7}{2^{+}}$ assignment for the $\Delta \mathrm{}\left(1950\right)\mathrm{}$ and established a $J^P=\frac{7}{2^{-}}$ assignment for the $N\left(2190\right)\mathrm{}$. It does not support a $J^P=\frac{11}{2^{+}}$ assignment for the $\Delta \mathrm{}\left(2460\right)\mathrm{}$, nor does it give support for some of the possible resonances found in the CERN phase-shift analysis. Apart from the resonance behavior, the partial-wave analysis reveals several new features. We find a striking correlation among the various partial-wave amplitudes at the highest energy, which is different for $J=l+\frac{1}{2}$ and $J=l-\frac{1}{2}$. In addition, several fixed-($-t$) features of high-energy scattering emerge in the energy region of this analysis.

Planar duality amplitudes are shown to have Regge asymptotic behavior when $\mathrm{}\left|s\right|\mathrm{}\to \infty$ at any non-vanishing angle to the real axis with $t$ fixed. The asymptotic behavior of the amplitudes in the same $s$ limit with $u$ fixed is also investigated.

The effect of the annihilation of nucleon-antinucleon pairs upon the process of matter-antimatter separation in blackbody radiation is considered. It is shown to be negligible if annihilation is correctly described by the statistical model.

Weinberg's approach to the high-energy behavior of chiral Lagrangians is applied to the process $\pi +\alpha \to 2\pi +\beta$, and it is shown that the algebraic relations required to give good asymptotic behavior in this process are the same as those which give good behavior in the reaction $\pi +\alpha \to \pi +\beta$.

Pfleegor and Mandel produced interference effects from two separate independent laser beams when the quanta arriving at the detector were separated in time by an average of about 1.4×${10}^{-7\mathrm{}}$ sec. If the quanta are photons (particles), then, to produce interference, each photon must store energy in the detector for an average of at least 1.4×${10}^{-7\mathrm{}}$ sec. But Jánossy and Náray have recently shown that over a period of 9×${10}^{-9\mathrm{}}$ sec there is no such storage, at least when the phases are random. Thus the result of Pfleegor and Mandel is in conflict with the corpuscular concept of visible light.

The kernel needed in the application of the unitarity condition in the Blankenbecler-Goldberger impact-parameter representation is reduced to a simple sum suitable for numerical work. We also comment briefly on a modified version of the representation.

We present a theory of the origin of the weak-interaction angle $\theta$, based on a self-consistency condition linking weak, strong, and electromagnetic symmetry-breaking effects. The value of $\theta$ is related to the observed pattern of breaking of $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$, and depends upon the value of a new parameter $\xi$, which gives the strength of the weak corrections to strong processes. A characteristic result of the theory is the prediction of a nonelectromagnetic isospin breaking. This solves the $\eta \to 3\pi$ puzzle and accounts for the observed deviation from the Dashen sum rule: ${m_K}^{+2\mathrm{}}-{m_K}^{02}={m_{\pi }}^{+2\mathrm{}}-{m_{\pi }}^{02}$. Although we are not able to give a theoretical evaluation of $\xi$ in a realistic model of weak interactions, a phenomenological determination of $\xi$ is proposed, based on the observed isospin-breaking mass splittings among pseudoscalar mesons. In this way we get the prediction $\theta \approx 0.25$, which is in good agreement with the experimental value.

We construct a model of the Veneziano type for $\pi A_1$ elastic scattering. We find that the imposition of factorization determines the model almost completely in terms of models for $\pi \pi \to \pi \pi$ and $\pi \pi \to \pi A_1$; and that the mere existence of a model for $\pi A_1\to \pi A_1$ constrains the model for $\pi \pi \to \pi A_1$. An off-shell continuation of the model consistent with the hard-pion formalism is given. The combination of this continuation with the constraint mentioned above ensures that the "constants" multiplying the Veneziano functions must depend explicitly on the four-momentum squared of the particle off the mass shell; and that the Adler consistency condition is satisfied by the vanishing of these constants at zero four-momentum rather than by a condition on the trajectory function or the external masses.

Using the multiperipheral integral equation in a factorizable approximation, we construct a simple model in which Regge poles and cuts can be studied. In a one-pole version of this model, we obtain a bootstrap of a Regge trajectory and residue function. In a two-pole version, we study the Pomeranchuk singularity for small $t$, and its relation to the Amati-Fubini-Stanghellini cut.

The $K_{l3\mathrm{}}$-decay form factors $f_{\pm }\mathrm{}\left(t\right)\mathrm{}$ are discussed from a phenomenological Lagrangian approach based on the notions of chiral dynamics and field-current identity. For the spin-zero fields, a real $\sigma$ model in $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ is considered. The vector and axial-vector fields are introduced as gauge fields in this model, which then preserves the concept of field-current identity. The model has been made general so that one can study the possibility of both the kinetic-energy-mixing and the mass-mixing models for the massive gauge fields. It is found that the strong vector-meson decays $\rho \to \pi \pi$ and $K^{*}\to K\pi$ and the weak $K_{l3\mathrm{}}$ decays form a consistent picture in this model. For comaprison with experiments, expressions of experimentally measurable quantities are first derived for the general case of simultaneous mass and kinetic-energy mixing. The results for these kinds of gauge-field model are then studied separately. It is found that the Glashow-Weinberg relation for $f_{+}\mathrm{}\left(0\right)\mathrm{}$ should be exact up to second order in symmetry breaking for a gauge-field model where the symmetry breaking is manifested only through changes in the kinetic-energy matrix $Z$ and the mass matrix $M$. Expressions for the corrections to the $K_{l3\mathrm{}}$ form factors due to the existence of the scalar mesons are derived. In the limit of the nonexistent $\kappa$ meson (i.e., $m_s\to \infty$ and $f_s\to 0$), all the results reduce to those of Lee. Some discrepancies between the present work and the work of other authors using the current-algebra techniques are discussed.

A convenient method is introduced to analyze the requirements imposed by the analyticity of the full helicity amplitudes on the structure of Regge poles and their residues at $t=0\mathrm{}$ for two-body-to-two-body reactions with general masses and spins. This method enables us to visualize the structure of daughter trajectories and conspirators clearly. Also, in practice, this method enables us to make the following derivation easily for reactions with arbitrary spins. (1) The most singular parts of the daughter and conspirator residues at $t=0\mathrm{}$ are calculated for unequal-mass-unequal-mass reactions and unequal-mass-unequal-mass reactions. Then, through factorization, the nonvanishing parts of the daughter and conspirator residues are obtained for the equal-mass-equal-mass reactions. They are identified with a one-Lorentz-pole expansion. (2) In calculating the daughter and conspirator residues, the analyticity requirements of both the $t$-channel and the $s$-channel helicity amplitudes are satisfied. Therefore, the conspiracy equations are shown to be satisfied explicitly. (3) The restrictions on the slopes of the daughter trajectories are also obtained. Their independence of the external masses and spins is shown. (4) The restrictions on the slopes of the conspirators are also calculated. We obtain an interesting new result: For a trajectory of quantum number $M$, at $t=0\mathrm{}$, the trajectories ${\alpha }_{+}\mathrm{}\left(t\right)\mathrm{}$ and ${\alpha }_{-}\mathrm{}\left(t\right)\mathrm{}$ are equal, and likewise their derivatives up to the $\mathrm{}(M-1\mathrm{})\mathrm{}\mathrm{th}$. Before carrying out all these calculations, all the $t$ factors of the Regge residue have to be determined. By introducing a quantum number $M$ in the unequal-mass-unequal-mass reactions, the $t$ factors of the parent as well as the daughter residues are uniquely determined using the conventional method of analyticity and factorization. This quantum number $M$ is identified to be the $O\left(4\right)\mathrm{}$ $M$ in the equal-mass-equal-mass reactions. We note that if the definition of the quantum number $M$ is not affected by the coincidence of $\alpha \mathrm{}\left(t\right)\mathrm{}$ with an integer at $t=0\mathrm{}$, then the trajectory $\alpha \mathrm{}\left(0\right)\mathrm{}$ will choose sense if $M<\mathrm{}\alpha \mathrm{}\left(0\right)\mathrm{}$ and choose nonsense if $M>\mathrm{}\alpha \mathrm{}\left(0\right)\mathrm{}$. At the end of the paper, a discussion is given on the implications for the group-theoretical approach to the Regge-pole theory.

Necessary and sufficient conditions for baryon spectral-function sum rules are obtained under the assumptions that (1) the equal-time commutator of the axial charges ${Q_5}^a\left(x_0\right)$ ($a=1, 2, 3$) and the nucleon field $\overline{\psi }\mathrm{}\left(y\right)\mathrm{}$ is given by $\left[{Q_5}^a\right(y_0), \overline{\psi }\mathrm{}(y\left)\right]=-r_A\overline{\psi }\mathrm{}\left(y\right)\mathrm{}{\gamma }_5{\tau }^a+(\Delta I=\frac{3}{2} \mathrm{terms})$ and that (2) the axial-vector current ${A_{\mu }}^a\mathrm{}\left(x\right)\mathrm{}$ is conserved. For each of these sum rules (enumerated by $n=1, 2, 3\dots$), the equivalence to $\int d^{3}z{〈{\left[{Q_5}^a\right(y_0), {\left[{\left(\frac{\partial }{\partial y_0}\right)}^{2n-1}\psi \mathrm{}\right(y), \overline{\psi }\mathrm{}(z\left)\right]}_{+}]|}_{y_0=z_0}〉}_0=0\mathrm{}$ is actually shown under weaker conditions: assumption (1) and, instead of (2), ${{\Sigma }_{j=0\mathrm{}}}^{2n-2}{〈{{\left[\right\{{\left(\frac{\partial }{\partial y_0}\right)}^j[\int d^{3}x{\partial }^{\mu }{A_{\mu }}^a\left(y_0\mathrm{x}\right), {\left(\frac{\partial }{\partial y_0}\right)}^{2n-2-j}\psi \mathrm{}(y\left)\right]\}, \psi \mathrm{}(z\left)\right]}_{+}|}_{y_0=z_0}〉}_0=0\mathrm{}$. Further equivalences are given. The sum rules connect the ($I=\frac{1}{2}$, $J={\frac{1}{2}}^{+}$) and ($I=\frac{1}{2}$, $J={\frac{1}{2}}^{-}$) baryon spectrum and include (for $n=1\mathrm{}$) a sum rule, obtained independently by Rothleitner and (in the one-particle approximation) by Sugawara. In our derivation we make no assumptions on high-energy behavior and we use an identity of the Jacobi type. Assuming the first two sum rules to be valid, the model then predicts a $P_{11}(m>\mathrm{}1470\mathrm{} \mathrm{MeV})$ resonance [which may be identified as the observed $P_{11}\mathrm{}\left(1750\right)\mathrm{}$] from the existence of the four nucleon resonances $P_{11}\mathrm{}\left(940\right)\mathrm{}$, $P_{11}\mathrm{}\left(1470\right)\mathrm{}$, $S_{11}\mathrm{}\left(1550\right)\mathrm{}$, and $S_{11}\mathrm{}\left(1710\right)\mathrm{}$.

A simple prescription is suggested for preserving universality of the isovector current in the presence of many $1^{-}$ poles ${\rho }_i$. By identifying $g_{{\rho }_{p-\gamma }}$ as proportional to $g_{{\rho }_i\pi \pi }$, predictions are made regarding (a) the modification of the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation, (b) charge radii, (c) $\pi \pi$ resonance production in colliding beam experiments, (d) high-energy $\rho$ meson photoproduction and photoabsorption, (e) photoproduction of ${\rho }^{\prime }$ and ${\rho }^{\prime \prime }$, and (f) asymptotic behavior of form factors.

Strong interactions of spin-zero and spin-one mesons are studied in a model in which the Lagrangian is approximately invariant under coordinate-dependent $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ gauge transformations. The scalar and pseudoscalar nonets are assigned to the (3,3*) ⊕ (3*,3) representation, whereas the vector and axial-vector octets are introduced as gauge fields belonging to the (1,8) ⊕ (8,1) representation. Spontaneous symmetry breaking to the isospin-hypercharge level is introduced by giving nonzero vacuum expectation values to some scalar fields. The effective Lagrangian obtained after considering field mixings and renormalizations is used in a phenomenological manner to study the masses and couplings of various particles. With some of the experimental meson masses as input, the predicted masses of remaining observed mesons are in reasonable agreement with experiment. Some scalar-meson masses are also predicted (${\mu }_{S_K}=527\mathrm{}$ MeV and ${\mu }_{S_{\pi }}=771\mathrm{}$ MeV). The widths for $V\to \mathrm{PP}$ and $A\to \mathrm{VP}$ decays are calculated and compare well with experiment. The axial-vector currents and the strangeness-changing vector currents satisfy partial conservation equations. Decay constants for spin-zero mesons are calculated. We get $\frac{F_K}{F_{\pi }}=1.17\mathrm{}$ and $\frac{F_{S_K}}{F_{\pi }}=-0.59\mathrm{}$. The $K_{l3\mathrm{}}$ form factors are calculated, the effect of the scalar kaon being included; we get $f_{+}\mathrm{}\left(0\right)=0.86\mathrm{}$, $\xi =-0.197\mathrm{}$, ${\lambda }_{+}=0.023\mathrm{}$, and ${\lambda }_{-}=0.013\mathrm{}$.

An $\mathrm{SU}\left(3\right)\mathrm{}$-symmetric multichannel calculation of the electromagnetic mass differences in the pseudoscalar-meson and baryon octets is carried out with an attempt to include some of the physics of the crossed (pair-annihilation) channel along the lines of the recent work by Ball and Zachariasen. The importance of the tensor-meson Regge trajectories is emphasized. The agreement with experiment is poor for the isospin-1 mass differences, but excellent for those with isospin 2.

The conditions for nondegeneracy of the leading trajectory in scalar-vector scattering are derived. They are applied to the Veneziano model for the pion contribution to the $\pi -\rho$ scattering amplitude. A general class of models for the double-charge-exchange process is found, and a "minimal" model is discussed in detail. The Adler self-consistency condition and its relation to the quantization rules of Ademollo et al. is discussed. The possible existence of exotic resonances or an $I=0\mathrm{}$ trajectory degenerate with the $\pi$ trajectory is also discussed.

A parametrization for Regge vertices is presented. These vertices have the most general $t$ dependence consistent with constraints at $t=0\mathrm{}$ and pseudothresholds, and are valid for general spins and general masses and for nonparallel trajectories. The assumptions upon which this work is based are analyticity, crossing symmetry, factorization (unitarity), and Regge asymptotic behavior. In the unequal-mass case, we find that the general Regge vertex has a particularly simple expansion around $t=0\mathrm{}$.