Spectral density of eigenvalues of the wave equation and vacuum polarization

Effective Lagrangian of the vacuum polarisation is expressed in terms of spectral density of eigen-values of the wave equation and five-dimensional Green function introduced by V. A. Fock in his method of the 5-th coordinate. Method can be applied for external fields of arbitrary strength but only if the interaction of vacuum fields is neglected. The calculations for the case of vacuum polarisation by gravitational and electromagnetic fields are performed.