Yurchenko

Relationship between tomographic representation of quantum mechanics in which quantum states are described by symplectic tomograms, and the theory of canonical quantization is discussed. As in quantum tomography, and in the theory of canonical quantization using linear canonical transformations. It is shown that the Bogolyubov transformation does not generalize the transformations used in quantum tomography. We consider the construction of second quantization in the tomographic representation and found that the density operator of a many-particle analog of the expression for the symplectic tomograms. As an example, solved the problem of a quantum chain of oscillators.