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A calculation of the inner Coulomb corrections to pionnucleon phase shifts is presented which does not depend on an expansion in powers ofkr0. The estimates obtained depend on the choice of simple, reasonable potential models. It is noted that the same corrections may be useful in analyzing other elementary particle reactions.

The question of the Reggeization of the elementary particles in renormalizable gauge theories with the Higgs-Kibble mechanism is examined. It is concluded that the massive non-Abelian gauge vector mesons and $J=\frac{1}{2}$ fermions of these theoreis lie on Regge trajectories in every case in which a counting criterion due to Mandelstam is satisfied. Several explicit examples are presented which verify that the necessary factorization condition of the Born helicity matrices is satisfied at $J=1$ and $J=\frac{1}{2}$, supporting this conclusion.

Methods are described for determining the leading light-cone singularities of bilocal operators in perturbation theory. Specific results are obtained for the bilocal operator ${T}^{*}{\ensuremath{\psi}(x)\overline{\ensuremath{\psi}}(0)}$ in the scalar-gluon model in lowest nontrivial order, with the finding that the $q$-number part of the bilocal operator is singular in the limit ${x}^{2}\ensuremath{\rightarrow}0$, contrary to usual assumptions. A description of the anomalies of deep-inelastic scattering is given in terms of canonically determined bilocal operators, with due attention to the singular nature of these operators, and with no recourse to new bilocal operators not present at the canonical level. Applications to the Schwinger-term sum rule and electromagnetic mass operator are made, with the same conclusions.

This review is concerned with the application of dispersion relation methods to direct nuclear reactions. We begin with a discussion of the assumptions required to relate analyticity properties to the conventional descriptions of direct-reaction amplitudes. This leads naturally to a description of phenomenological methods such as extrapolation to poles and similar topics. The use of the unitarity condition provides a framework for the discussion of the distorted wave Born approximation from the $S$-matrix point of view Finally we call attention to some dynamical calculations of relevance to our discussion.

The process π− + p → K° + Λ is studied near threshold by means of a resonance model based on the Cini-Fubini approximation using only known resonances. Thus the only term contributing an imaginary part to the amplitude is the N∗(1688) T = 12, F52+ resonance. Reasonable agreement with the total cross-section and angular distribution data is obtained, but the predictions for the polarization are not satisfactory. It is concluded that either several small, complex amplitudes make important contributions to the polarization, or that there are other large partial waves in addition to the F52 resonance. It may be difficult to distinguish between these two possibilities within the framework of this or other conventional resonance models.

A model for the reaction $\ensuremath{\pi}+N\ensuremath{\rightarrow}2\ensuremath{\pi}+N$ at low energies, with $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering lengths as parameters, discussed in a previous analysis is extended by removing the assumption that $\frac{{a}_{0}}{{a}_{2}}=\frac{5}{2}$. The parameters are determined by using the ${\ensuremath{\pi}}^{+}$ angular distribution from ${\ensuremath{\pi}}^{\ensuremath{-}}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}+{\ensuremath{\pi}}^{+}+n$ at 430 Mev and the total cross section for ${\ensuremath{\pi}}^{+}+p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{+}+n$ at 470 Mev. We find two acceptable sets for the $\ensuremath{\pi}\ensuremath{-}\ensuremath{\pi}$ scattering lengths: ${a}_{0}=0.50$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$, ${a}_{1}=0.07$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$, ${a}_{2}=0.16$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$ and ${a}_{0}=0.65$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$, ${a}_{1}=0.07$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$, ${a}_{2}=\ensuremath{-}0.14$ ${\mathrm{\ensuremath{\mu}}}^{\ensuremath{-}1}$. The total cross sections for the various charge channel and for single partial waves are computed. The predictions of this model are in qualitative agreement with experiment.

A Skyrme-model calculation of weak radiative baryon octet and decuplet decays is presented, based on a Lagrangian describing weak nonleptonic decays of mesons previously discussed by Donoghue and collaborators. There are no free parameters in the Skyrme-model predictions for weak radiative decays, as all necessary parameters are obtained from other contexts. The predictions of the Skyrme model for the weak radiative baryon decays are in good qualitative agreement with experiment, except for ..sigma../sup +/..-->..p..gamma.., where however the model involves substantial cancellations among terms which are sensitive to small changes of input parameters.

Possible topological solitons (skyrmions) of four-dimensional supersymmetric nonlinear σ-models are investigated. The requirements of supersymmetry limit our study to the CP 1 model. A stable soliton seems possible, but in the absence of a demonstrated lower-bound for the mass, the stability of the soliton is unproved. The semi-classical spectrum of the CP 1 skyrmion, as well as its supersymmetric extension, is studied.

An effective Hamiltonian for the spin‐dependent interactions in quarkonium is defined. The relevant effective interactions are extracted from the data in a nearly model independent way, without reference to specific models. The systematic behavior of the spin‐dependent qq interactions is noted.

We describe here some recent work1 in which we undertook to investigate, based on the dynamics of N=8 supergravity, the existence of bound states in this system. We were motivated to some extent by the suggestion of Ellis, Gaillard, Maiani and Zumino2 (EGMZ) that N=8 supergravity could make contact with current particle phenomenology if one postulated a certain set of massless (before symmetry breaking) bound states transforming according to the local SU(8) invariance group that the theory may possess3. In their original proposal EGMZ assumed that these bound states had the quantum numbers of a so-called “current multiplet”: $${\left( { - 3/2} \right)_{\text{L}}},\;\left( { - 1} \right)_{\text{L}}^{\text{A}},\; \cdots \;\left( {5/2} \right)_{\text{L}}^{{\text{AB}}}\; \cdots \; + \left( {{\text{TCP}}\;{\text{conjugates}}} \right)$$ The particles of SU(5) GUT were to be found among these, following a sequence of symmetry breakings. It has also been argued” that in order to make the EGMZ scenario viable, one might have to postulate an infinite tower of massless particles.

The status of decoupling theorems and effective field theories is reviewed. It is emphasized that decoupling is valid for minimal subtraction if an effective field theory with appropriate effective couplings is constructed.

Further discussion of the hadronic corrections to the van Royen--Weisskopf formula is presented.