Hamiltonian Approach to Secondary Quantization

Abstract—Structures and objects used in Hamiltonian secondary quantization are discussed. By the secondary quantization of a Hamiltonian system $\mathcal{H}$, we mean the Schrödinger quantization of another Hamiltonian system ${{\mathcal{H}}_{1}}$ for which the Hamiltonian equation is the Schrödinger one obtained by the quantization of the original Hamiltonian system $\mathcal{H}.$ The phase space of ${{\mathcal{H}}_{1}}$ is the realification ${{\mathbb{H}}_{R}}$ of the complex Hilbert space $\mathbb{H}$ of the quantum analogue of $\mathcal{H}$ equipped with the natural symplectic structure. The role of a configuration space is played by the maximal real subspace of $\mathbb{H}$.