Generating functional $Z_0$ for the one-wormhole sector

We proceed in constructing a quantum theory of wormholes by adapting the method of Gervais, Jevicki, and Sakita. We calculate the transition amplitude for one-wormhole processes and separate the motion of the wormhole in the tree approximation: it is the motion of a free relativistic particle with the mass $\frac{m}{G}$, the classical mass of the wormhole. The quantum corrections can be calculated from the generating functional $Z$ for the Green's functions. We derive a formula for the zero approximation $Z_0$ to this functional, find a suitable gauge which simplifies the formula, and show that this gauge is compatible with our boundary conditions. The problem of zero modes is solved and a regular propagator is shown to exist. Finally, we estimate the cross section for the capture of photons and gravitons by a wormhole and find that it increases with energy reaching the value ${\mathrm{}\left(4m\right)\mathrm{}}^2$ asymptotically.