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A general relativistic and nontopological soliton is constructed by coupling a nonlinear scalar field to the standard gravitational field. Our results replicate the basic features of the special relativistic case: namely, a singularity-free lump with a discrete spectrum of eigensolutions. The central singularities and horizon that appear in the black hole solitons of string theory are not present.

An $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ effective Lagrangian, generated by a massive vector field, has been formulated with the aid of the group-geometrical method employed in our earlier papers. This formalism is manifestly invariant under nonlinear transformations, and permits an exact and compact treatment of the non-linearities. Our $\mathrm{SU}(3)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(3)$ treatment incorporates only those minimal departures from $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ that are required to secure a reasonable model, and the new Lagrangian contains no free parameters not already present in the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ model. These parameters are determined by fitting the linearized theory to the pion-nucleon system. Results for other members of the octets, such as the Callan-Treiman formula, are then in satisfactory agreement with experiment or with the current algebra. It is hoped that the formalism will permit the treatment of the nonlinearities to be extended beyond the discussion of the tree diagrams.

If the interaction Lagrangian contains derivatives, or if the spins of the interacting particles \ensuremath{\ge} 1, then both the propagators and the interaction Hamiltonian contain normal-dependent terms. Lee and Yang showed that if the noncovariant part of the propagator is dropped, then the finite interaction Hamiltonian is modified. In addition, there appears a term that is divergent, anti-Hermitian, and generally noncovariant if it does not vanish, namely, $\ensuremath{\delta}H=\frac{1}{2}i\ensuremath{\hbar}{\ensuremath{\delta}}^{4}(0)\ifmmode\times\else\texttimes\fi{}\mathrm{ln}\mathrm{det}g$, where $g$ depends on the structure of the theory. For massive gauge theories we have shown that $\ensuremath{\delta}H=0$ and that ${H}_{\mathrm{int}}=\ensuremath{-}{L}_{\mathrm{int}}$. These theories are manifestly covariant and the ordinary Feynman rules hold. Renormalization is not discussed.

It has been shown that the full Einstein field equations may be linearized and written in Lorentz-covariant form if the metric is of the Kerr-Schild form. It is here remarked that the Maxwell and Hamilton-Jacobi equations and also a restricted form of the Dirac equation have similar properties.