Classical action functional for the system of fields and wormholes

We lay down foundations of the quantum theory of wormholes for the model Einstein-Maxwell system. The generalization of the quantum theory of solitons to wormholes is not straightforward, because the fields are singular at $r=0\mathrm{}$. We propose to cut away the nonphysical part of the spacetime along the horizons and to impose boundary conditions at the resulting boundary of Cauchy surfaces. The boundary conditions are chosen such that (a) there is an action functional for the fields, (b) Poisson brackets of the boundary-fixed quantities with each other vanish, and (c) the soliton solution is unique. We study the action functional, find the surface terms, and, using the method of Regge and Teitelboim, extract the motion of the soliton. We show how the gauge group of the system is extended and find some properties of the additional gauge conditions. Finally, the soliton solution is written in the form in which all boundary and gauge conditions are satisfied.