Search

The two-nucleon interaction, via the exchange of scalar mesons, is examined in a nonperturbative manner. 'Schrödinger' equations are derived, and nonlocal potentials arise naturally. Both scattering and bound states are examined. A half-off-shell T matrix is obtained, and corresponding phase shifts are evaluated. In the bound state, a variational calculation is employed to determine the coupling constant.

An earlier paper examined the role of scalar mesons in the nucleon–nucleon interaction. A more realistic model, with pseudoscalar mesons, is studied here. Unlike previous treatments of this problem, this approach seems to yield more repulsion than would be required to reproduce experimental data. Calculations are performed on the spin singlet, isospin triplet state; a brief discussion of the deuteron channel and the resulting potentials is also included.

We show that a free spin 3/2 theory of the Pauli–Fierz type displays nonlocal structure. Similarly, a spin 1 theory coupled via an electric quadrupole to an external field also shows nonlocal structure. This is in sharp contrast to the cases of spin 0, 1/2, and 1 which do not have any nonlocality even in the presence of minimal coupling to an electromagnetic field. This leads us to conjecture that the acausal propagation discovered for spin 3/2 and spin 1 is due to additional structure of these fields.

A pair of sets of first-order differential equations is given. They contain as special cases all the known spin 1 theories except the Stueckelberg formalism. It is also known that all of these theories are essentially causal.

We consider a Dirac particle in 1 + 1 dimensions interacting with an external Coulomb potential and prove that this potential produces no bound states at all.