ИСТИНА

The primary Hamiltonian (or Schroedinger) (qp)-quantization is the transition from one (finite-dimensional or infinite-dimensional) Hamiltonian system (of ordinary differential equations with the Hamiltonian function H=H_0 on the phase space E_0 = Q_0 x P_0 ) to another one in such a way that for the new system the phase space E_1 is a Cartesian quare of the real L_2 space over Q_0 and the new system itself coinsides with the Scroedinger equation describing the evolution in the corresponding complex L_2(E_0) ~ E_1 for which the Hamiltonian operator H^ is a pseudo-differential operator with the (qp)-symbol H_0. O.G.Smolyanov supposed the definition of the Hamiltonian second quantization as the second iteration of the Hamiltonian primary quantization. For the case when H^ has discrete spectrum and H(q_0,p_0) is a sum K(p_0)+V(q_0), the correspondence with the Fock's secondary quantization is established.