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Hamiltonian approach to secondary quantization. (English. Russian original) Zbl 1410.81029
Dokl. Math. 98, No. 3, 571-574 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 483, No. 2, 138-142 (2018).
Summary: 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 $$\mathbb{H}$$.

##### MSC:
 81S30 Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81V70 Many-body theory; quantum Hall effect 81T05 Axiomatic quantum field theory; operator algebras 70H05 Hamilton’s equations 81S05 Commutation relations and statistics as related to quantum mechanics (general) 81S10 Geometry and quantization, symplectic methods
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