Pion-nucleon scattering up to a pion laboratory kinetic energy of 700 MeV is described by a Poincaré invariant, instant form model. The model is constructed in a space spanned by single-baryon states ͉B͘, where B is the nucleon, or any resonance that contributes in the energy range considered; and by meson-baryon states ͉B͘, where ͉B͘ϭ͉N͘, ͉⌬͘, or ͉N͘. The model specifies a mass operator in the form M ϭM 0 ϩU, where M 0 is a noninteracting mass operator and U contains the interactions. The ͗N͉U͉N͘ potentials are derived from N, ⌬, , and exchange processes. The vertex interactions ͗B͉U͉BЈ͘ are derived from field theory interaction Hamiltonians. Coupling to the inelastic channels, ͉⌬͘ and ͉N͘, is provided by a ͗N͉U͉⌬͘ transition potential due to nucleon exchange; and by interactions of the form B⇔BЉ⇔ЈBЈ.

On the basis of exact separable potential calculations, we show that there is a significant variation of the asymptotic normalization parameter C, of the triton with its binding energy. We present a partial wave dispersion relation technique for determining this parameter from the triton energy, the doublet n-d scattering length, the doublet, s-wave, n-d inelasticities, and the two-nucleon, on-shell scattering amplitudes. We test the method and find it to be accurate and stable with only low-energy information used as input. For a doublet scattering length of 0.65 fm we obtain C, = 3.3+0.1, where the error limits are determined from uncertainties in the inelasticities and the analytic continuation of the two-nucleon amplitudes to negative energies. I NUCLEAR REACTIONS exact separable potential calculations; partial wave dispersion r'elations for n-d elastic scattering amplitudes.

The Hamiltonian form of the Klein–Gordon equation is used to study the Zitterbewegung of spin- zero particles. It is shown that the time dependence of the velocity and position operators in the Heisenberg picture is formally the same as that of a spin- 1/2 particle. It is also shown that the Zitterbewegung is the result of the interference between positive and negative energy states. A representation-free expression is found for the mean position operator. This operator is free from Zitterbewegung. The Klein–Gordon equation is solved with an electrostatic potential originally used by Sauter in his investigation of the Klein paradox for spin- 1/2 particles. It is shown that the transmission to states with negative kinetic energy is very small when the electric field is weak.

A general formalism is established for constructing models for the photoproduction of mesons from the nucleon. The essential ingredient is a mass operator which describes the coupling between meson-baryon, photon-baryon, and single-baryon channels. The most general forms for the mass operator interactions which produce these couplings are derived. These forms also provide generalizations of the Chew-Goldberger-Low-Nambu amplitudes for pion-nucleon photoproduction to any meson-baryon final state. The models lead to S-matrix elements that transform properly under inhomogeneous Lorentz transformations and are gauge invariant. The photoproduction amplitudes include final state interactions and satisfy Watson's theorem. A specific model is constructed by deriving the mass operator interactions from effective Lagrangians that describe the couplings of mesons, photons, and baryons. The electromagnetic interactions include direct and crossed nucleon contributions, as well as direct contributions from the P 33 ͑1232͒, P 11 ͑1440͒, D 13 ͑1520͒, and S 11 ͑1535͒ resonances. A contact term and exchange terms due to the , , and mesons are also included. The model gives a good fit to the significant multipoles in the energy range from the single-pion, photoproduction threshold up to a center-of-momentum energy of W=1550 MeV, which corresponds to a photon lab energy of 810 MeV.

The existence of a virtual state of the three nucleon system is established on the basis of three diAerent analyses. Values for its pole position and residue in the doublet, s-wave, n-d elastic scattering amplitude, are obtained from a fit to the experimental data, from partial wave dispersion relations, and from an exact three-particle, separable potential calculation. The calculations indicate that these parameters are determined mainly by the one-nucleon exchange mechanism and the doublet scattering length a,. For a, = 0.65 fm our best calculation gives an energy of 0.482 MeV below the elastic threshold, on the second Riemann sheet, and a residue parameter C, = 0.0504, where C"' is defined in analogy to the triton asymptotic normalization parameter.NUCLEAR REACTIONS Three-nucleon virtual state; fits to data; dispersion relations; separable potential calculations.