Calculation of quantum corrections to non-trivial classical solutions by means of the zeta-function

Method of calculating functional determinants using zeta-function is considered. It is shown that the method can be efficient even when solving quantum-mechanical problems. Application of the given method to quantum-field problems allows one to easily calculate quantum corrections to non-trivial classical solutions. Calculation of quantum corrections to soliton mass, surface density of wall energy and to false (metastable) vacuum decay probability is considered as an example. All the calculaions are referred to the case of zero temperature, but however, zeta-function method considered may be generalized taking into account the case of final temperature, and applied to considering the phase transition processes at an early stage of the Universe evolution