Bogoliubov quasiparticles in constrained systems

This paper is devoted to the formulation of quantum field theory for an ear ly universe in general relativity, considered as the Dirac general constrai ned system. The main idea is the Hamiltonian reduction of the constrained s ystem in terms of measurable quantities of the observational cosmology: the world proper time, cosmic scale factor, and the density of matter. We defi ne 'particles' as field variables in the holomorphic representation which d iagonalize the measurable density. The Bogoliubov quasiparticles are determ ined by diagonalization of the equations of motion (but not only of the ini tial Hamiltonian) to get the set of integrals of motion (or conserved quant um numbers, in quantum theory). This approach is applied to describe partic le creation in the models of the early universe where the Hubble parameter goes to infinity.