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The method of functional integrals is applied to the problem of meson theories with derivative couplings. In the static limit, solutions in closed form can be exhibited. The infinities occurring in the theory are found to be removable in terms of Z_2 and mass renormalizations, contrary to the conclusions of perturbation analysis. The divergences occurring here have the form of essential singularities, in contradistinction to the branch-point behavior of the usual "renormalizable" theories. The lack of validity of the perturbation expansion is thereby accounted for. These techniques can be extended to treat the full recoil neutral ps(pv) problem omitting closed loops. The theory is represented in terms of an exponential coupling which permits a nonperturbation series solution for the various propagators. Two infinite renormalizations are again required. The resultant functions are given meaning by analytic continuation procedures which are adapted to the four-dimensional nature of the problem. The form of the effective coupling suggests a rearrangement of the answer in terms of exponentials of the meson propagator. As a result mass operator-like structures can be defined. These explicitly exhibit the transcendental nature of the coupling and generalized equivalence theorems with ps(ps) theory can be generated. In a similar fashion, effective interaction operators for the two-nucleon and meson-nucleon Green's functions are derived. The possible applicability of these quantities to questions of physical interest such as nuclear potentials and multiple meson production is briefly mentioned. In an appendix, a model of beta coupling is discussed in connection with the renormalization question there.

From the physical three-vector Maxwell equations for an electromagnetic (E.M.) field in static gravitation, we examine the artifice of replacing the gravitation by an equivalent medium and we find modified Debye potentials for an E.M. wave in a simple, angularly homogeneous, material medium in a Schwarzs-child gravitational field. The fact that these potentials do not obey the generalized scalar wave equation implies that gravitation scatters the vector E.M. wave and a scalar wave differently. Also, we obtain and solve by perturbation the amplitude and eikonal equations for a high-frequency wave in a weak spherical gravitational field. To the order $\frac{M}{r}$, the state of transverse polarization does not change along a ray path whereas the transverse-field amplitudes are modified by the factor ${e}^{\frac{M}{r}}$ which strengthens the field near the mass. The longitudinal-field amplitude, on the other hand, is modified by ${e}^{\frac{\ensuremath{-}M}{r}}$. These effects, in principle, may provide a further test of classical E.M. theory and general relativity.

The Hamiltonian form of the relativistic wave equation for bosons of spin 0 or 1 was first given by Kemmer. The problems associated with the redundant components of the wave function were later resolved by Heitler, who eliminated the redundant components by means of projection operators. We present an alternative treatment which yields essentially the same results as obtained by Heitler, but which retains all components of the wave function. Approved for public release; distribution is unlimited.

Two generalizations of Sugawara models are discussed. In the first, new interactions are introduced by altering the current commutators but retaining the "free" form of T_(μν), as exemplified by a simple effective π^0 − 2γ interaction, which is compared with the standard triangle-diagram results. The second permits non-quadratic T_(μν), which retain the "algebra" part of the current commutators; these models avoid the Dashen-Frishman parity degeneracy.

In the dual resonance model, introducing a generalized gauge-transformation operator which leaves the vertex functions invariant, we present a general treatment of linear dependences among the vertex functions. We also prove that the two propagators recently discussed in connection with the twisting operator are equal up to our gauge transformation.