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

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12

Canonical anti-commutation relations

Throughout this chapter, (, ν) is a Euclidean space, that is, a real vector space equipped with a positive definite form ν.

In this chapter we introduce the concept of representations of the canonical anti-commutation relations (CAR representations). The definition that we use is very similar to the definition of a representation of the Clifford relations, which will be discussed in Chap. 15. In the case of CAR representations we assume in addition that operators satisfying the Clifford relations act on ...

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