On the theory of cavities with point-like perturbations. Part I: General theory

The theoretical interpretation of measurements of wavefunctions and spectra in electromagnetic cavities excited by antennas is considered. Assuming that the characteristic wavelength of the field inside the cavity is much larger than the radius of the antenna, we describe antennas as point-like perturbations. This approach strongly simplifies the problem reducing the whole information on the antenna to four effective constants. In the framework of this approach we overcame the divergency of series of the phenomenological scattering theory and justify assumptions lying at the heart of wavefunction measurements. This selfconsistent approach allowed us to go beyond the one-pole approximation, in particular, to treat the experiments with degenerated states. The central idea of the approach is to introduce ``renormalized Green function, which contains the information on boundary reflections and has no singularity inside the cavity.