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Mathematics of Quantization and Quantum Fields by Christian Gérard, Jan Derezinski

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9

CCR on Fock space

This chapter is devoted to the study of the Fock representation of the canonical commutation relations. This representation is used as the basic tool in quantum many-body theory and quantum field theory. Unlike the Schrödinger CCR representation, it allows us to consider phase spaces of infinite dimension.

Throughout this chapter, is a Hilbert space. This space will be called the one-particle space. The Fock CCR representation will act in the bosonic Fock space Γs ().

As in Sect. 1.3, we introduce the space

which will serve ...

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