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

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11

Symplectic invariance of the CCR on Fock spaces

This chapter is a continuation of Chap. 9, where we studied Fock CCR representations. Our goal is to extend the results of Chap. 10 about the symplectic invariance of canonical commutation relations to the case of Fock CCR representations in any dimension.

11.1 Symplectic group on a Kähler space

The basic framework of this section, as well as most other sections of this chapter, is the same as that of Chap. 9.

In particular, throughout the section, (, ·, ω, j) is a complete Kähler space. We recall that for r B(), r# denotes the adjoint of r for the Euclidean scalar product of .

Recall that the ...

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