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

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16

Orthogonal invariance of the CAR on Fock spaces

In this chapter we continue our study of the orthogonal invariance of the CAR. This invariance was already investigated in Chap. 14. However, whereas in Chap. 14 we used the representation-independent framework of CAR algebras, in this chapter we will consider Fock CAR representations in any dimensions. Therefore, to some extent, this chapter can be viewed as a continuation of Chap. 13 about Fock CAR representations.

Note also that this chapter is parallel to Chap. 11 about the symplectic invariance of the CCR on a Fock space.

16.1 Orthogonal group on a Kähler space

The framework of this section, as well as of most other sections of this chapter, is the same as that of Chap. 13 about the Fock ...

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