Previous treatments on high-energy scattering in quantum electrodynamics are extended to diffractive inelastic processes. We explore the model in which the diffractive excitation proceeds through the exchange of vector mesons. Six inelastic impact factors are explicitly calculated in the lowest order: (1) scalar to scalar, (2) pseudoscalar to pseudoscalar, (3) vector to vector, (4) axial vector to axial vector, (5) scalar to axial vector, and (6) pseudoscalar to axial vector. For all six of these impact factors, the masses of the incoming and outgoing particles may be different; and for the last two impact factors, the spins and the parities of the incoming and outgoing particles may be different. The nonvanishing of the impact factors demonstrates that mass, spin, and parity can change during a diffractive process. We also conclude that $C$ (charge conjugation quantum number), $S$ (strangeness), $I$ (isotopic spin), $B$ (baryon number), and $G$ parity, etc., must remain the same during a diffractive process. Some general properties of the impact factor are also discussed.

Production amplitudes in quantum electrodynamics are studied in the high-energy limit. In particular, we calculate the impact factors for pair production and for bremsstrahlung explicitly. Numerous production amplitudes are then obtained in terms of these two impact factors. The method we use is the one of impact diagrams, which is applicable to all Feynman diagrams at high energies.

The discontinuity of the Regge trajectory obtained recently from a duality series by Kikkawa, Sakita, and Virasoro is investigated. The trajectory is shown to possess all the thresholds corresponding to two-particle intermediate states, i.e., Regge recurrences or daughters. A correction to a linear trajectory is also shown to arise by requiring the Born term (the Veneziano amplitude) to be modified to satisfy two-body partial-wave unitarity near the leading pole in the $J$ plane. This discontinuity is evaluated up to the third two-particle threshold and found to be identical to that obtained from the duality series. Above higher thresholds, such agreement is dependent on the function used to ensure factorization at internal vertices in each term of the duality series.

With the aid of a covariant spin formalism, the kinematic constraint equations for helicity amplitudes are studied in a systematic way for all mass configurations, including the case of zero-mass particles. The complete set of constraints at thresholds and pseudothresholds is given in a form convenient for calculation; that is, the coefficients of the helicity amplitudes are simple numerical ones (as opposed, for instance, to $D$ functions). For nonzero-mass particles, the reduction of the constraints in terms of total spin amplitudes is shown to follow. Amplitudes with different values of total spin are not related at thresholds or pseudo-thresholds.

In the usual method of regularization, the regulator axial-vector current is not conserved. Consequently, the regularized axial-vector current does not, in general, satisfy the ordinary divergence equation derived by using field equations. The anomalous axial-vector divergence equation of spinor electrodynamics is shown to be related to this difficulty of regularization. Using the chiral-invariant regularization and the generalized renormalization procedure developed previously, we show how to obtain an axial-vector vertex which obeys the normal Ward-Takahashi identity and is renormalizable to all orders of perturbation theory. Our general argument is illustrated by an explicit calculation of the fourth-order contribution to the axial-vector vertex from the anomalous triangle loop diagram. We also observe that the renormalized axial-vector vertex, which is well behaved from the point of view of perturbation theory, violates the requirement of generalized unitarity.

Constructing particles out of quarks (via infinite-component fields), we show that if an "elementary" particle has integral spin, baryon number $B\ne 0$, and a symmetric spin-isospin wave function, then its electromagnetic charge form factor vanishes.

Certain of the Reggeized Feynman diagrams suggested by Kikkawa, Klein, Sakita, and Virasoro that require integrals of infinite products of functions are examined. Methods are formulated for explicitly evaluating the infinite products that occur in simple examples of the class of one-loop nonplanar Reggeized Feynman diagrams whose duals are homeomorphic to a sphere with two windows. The infinite products are found to cause the integrals in these cases to diverge, necessitating a regularizing procedure. The integrals can be given meaning by a redefinition which produces an unwanted pole in the square of the sum of the momenta associated with either window, or with a certain type of smoothing function.

The relation between the algebra of current densities and the finite- or infinite-component wave equations is critically investigated. It is found that, at any arbitrary momentum, the charge-current density commutation relations can be satisfied by the solutions of the wave equation, but only in a trivial sense, viz., if $J_0\mathrm{}\left(0\right)\mathrm{}$ is taken to be unity, in which case the content of the current commutators is essentially 1. $J_{\mu }\mathrm{}\left(k\right)=J_{\mu }\mathrm{}\left(k\right)\mathrm{}$, i.e., empty. Furthermore, it is shown explicitly in an example that, starting from the covariant wave equation, this condition $J_0\mathrm{}\left(0\right)=1\mathrm{}$ can be satisfied only if it is made true by definition. The precise connection between the current algebra and infinite-component wave equations is discussed by the introduction of translation operators in momentum space.

The general theory of the propagation of pulse disturbances in an unstable, slightly inhomogeneous, and time-dependent medium is derived in complementary fashion to the eikonal theory of the propagation of stable waves. For a dispersion $D(\mathrm{k}, \omega ; \mathrm{a})$, where k is the wave number and $\omega$ is the (complex) frequency which is related to k for given values of the auxiliary parameters a (temperature, density, etc.) by the vanishing of $D$, the rate of change of propagation velocity of an element of the disturbance is found to be $\frac{\mathrm{dV}}{\mathrm{da}}=\mathrm{Re}(-\frac{D_{\mathrm{a}}}{k{D}_{\omega }})$ in one dimension. A similar equation holds in the case of a general $n$-dimensional system. This relation makes possible the construction of the complete pulse shape in fairly simple fashion for the case of a general slowly varying medium. The theory is illustrated by application to a particular unstable dispersion.

Coherence properties of the single-mode electromagnetic radiation emitted by a system of identical two-level atoms which is initially in the superradiant state are determined approximately. The approximation is valid only for short times when the state of the atomic system does not differ appreciably from the superradiant state. The electromagnetic field radiated spontaneously possesses full coherence in the sense of Glauber's definition, its density operator having the form of that for the ideal laser radiation. This coherence disappears when, because of external radiation, stimulated and spontaneous emission both take place.

The amplitude of adiabatic perturbations that might have existed in the early universe is limited by the nonlinear transfer of energy to high frequencies. For flat cosmological models, this limit, together with the effect of linear dissipation, yields a residual perturbation in the matter distribution comparable with the semiempirical estimate of what is needed to produce massive galaxies.

Long-range weak-interaction forces arising from multiple neutrino exchange do not significantly affect the evolution of a homogeneous, isotropic universe. Inhomogeneities can induce an effective local $\frac{1}{r^2}$ force between electrons but the magnitude of this force is much smaller than gravity for our universe.

The energy per particle in a many-particle system, both for bosons and fermions, is discussed using a perturbation method and some results on reduced density matrices obtained previously. The theory is tested for hard-sphere, Lennard-Jones, and nonsingular potentials; it exhibits clearly the difficulties in going to higher-order approximations and gives results which correspond to those obtained by other methods.

Beginning with the definition of a duplicated experiment and the fact that the resulting data are summarized as a set of configurations of some observables, together with frequencies of occurrence of each configuration, we derive the formal structure of conventional quantum theory using only the statistical properties of such data, and show that certain elements of the theory have heretofore been overlooked. This derivation yields a rather broad generalization of the theory which suggests new methods for describing phase transitions and possibly fundamental particles as well.

The propagation of electromagnetic waves in a Fermi sea of neutrinos is investigated on the basis of the photon-neutrino weak-coupling theory and is compared with the result obtained by Royer on the basis of the $\left(e\nu \right)\left(e\nu \right)$ coupling. It is shown that a photon propagating through the neutrino sea satisfies a dispersion relation of the form ${\omega }^2={{\omega }_0}^2+k^2{c}^2$, where ${\left(\hslash {\omega }_0\right)}^2\approx 6.2\times {10}^{-23\mathrm{}}$ ${E_F}^2$, $E_F$ being the Fermi energy of the sea. Finally, some remarks are made as to the possibility of the destruction of a photon when propagating through the sea due to the process $\gamma +\nu \to \nu +\nu +\overline{\nu }$. It is found that the mean free path corresponding to this process is ≈ ${10}^{69}$ cm, much larger than the radius of the universe.

The orbital angular momentum of the $A_1$ meson produced from ${\pi }^{-}p\to {\pi }^{-}{\pi }^{-}{\pi }^{+}p$ at 16 GeV/c was studied by analyzing the decay angular distributions in the ${\rho }^0{\pi }^{-}$ state. A completely Bose-symmetrized formalism was used to measure the ratio $\frac{g_1}{g_0}$ of the helicity states of the $\rho$ from the $A_1$ decay. The value obtained, $\left|\frac{g_1}{g_0}\right|=0.48\mathrm{}\pm 0.13$, indicates a substantial $d$-wave contribution in the $A_1$ decay.

We show that the Veneziano-Lovelace one-term formula for pion-pion scattering, although a good first approximation, has some undesirable features. With the help of a few secondary terms, a model amplitude, which is consistent with the known properties of the pion-pion system up to the $f^0$ mass region and the high-energy phenomenology, is constructed.

The radiative decays of the $X^0$ meson are analyzed in the framework of an effective Lagrangian with vector-meson dominance, using vector gauge fields with current mixing and assuming $X^0$ to be a unitary singlet. The underlying $\mathrm{VVP}$ strong interaction obeys octet-broken $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry. The model is shown to predict branching ratios different from those obtained in the $\eta -X^0$ mixing model. An analysis of the experimental situation is presented, and the relevance of the $X^0\to 2\gamma$, $X^0\to \omega \gamma$ partial decay modes for distinguishing between different theoretical models is pointed out.

We present the decay characteristics of the low-mass $Q^{+}$ enhancement in the ${\left(K\pi \pi \right)}^{+}$ system which is produced in the reaction $K^{+}p\to {\left(K\pi \pi \right)}^{+}p$ at 12.7 GeV/c. When treated as a single resonance, this enhancement has the properties expected for the strange member of an $\mathrm{SU}\left(3\right)\mathrm{}$ meson octet with $J^{\mathrm{PC}}=1^{++}$. The resonance position and width of the $Q$ are, respectively, 1260±20 and 180±20 MeV.

The properties of the hypernucleus ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ were measured in an analysis of helium-bubble-chamber pictures taken at the Argonne ZGS. Some 90 examples of the production reaction $K^{-}+{\mathrm{He}}^4\to {}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}+p+{\pi }^{-}$ were found in which the $K^{-}$ stopped and the ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ decayed via ${\pi }^{-}$ emission. Twenty-seven events were observed to decay via the two-body mode ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}\to {\pi }^{-}{\mathrm{He}}^3$, with the remaining events decaying to ${\pi }^{-}\mathrm{pd}$ or ${\pi }^{-}\mathrm{ppn}$. The production rate was measured to be (${1.8}_{-0.6\mathrm{}}^{+0.7\mathrm{}}$)×${10}^{-3\mathrm{}}$ per stopping $K^{-}$. The mean life of the hyper-fragment was measured from the two-body decay mode as (${2.64}_{-0.52\mathrm{}}^{+0.84\mathrm{}}$)×${10}^{-10\mathrm{}}$ sec. The lifetime obtained from the three-body decays was consistent with this value, after the elimination of a serious source of background. The binding energy of ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ was measured to be 0.25±0.31 MeV. The decay ratio $R_3=\frac{\Gamma ({}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}\to {\pi }^{-}{\mathrm{He}}^3)}{\Gamma ({}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}\to \mathrm{all} {\pi }^{-})}$ was measured to be ${0.36}_{-0.06\mathrm{}}^{+0.08\mathrm{}}$, in agreement with values from previous experiments and with the value calculated for spin ½ for the ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ hypernucleus.