39.6 For further reading
Concept links · terms present in this machine draft; source roles are unverified: Lie algebra
Berezin’s The Method of Second Quantization [6] develops in detail the infinite dimensional version of the Bargmann-Fock construction, both in the bosonic and fermionic cases. Infinite dimensional versions of the metaplectic and spinor representations are given there in terms of operators defined by integral kernels. For a discussion of the infinite dimensional Weyl and Cliford algebras, together with a realization of their automorphism groups and (and the corresponding Lie algebras) in terms of annihilation and creation operators acting on the infinite dimensional metaplectic and spinor representations, see [64]. The book [70] contains an extensive discussion of the groups and and the infinite dimensional version of their metaplectic and spinor representations. It emphasizes the origin of novel infinite dimensional phenomena in the geometry of the complex structures used in infinite dimensional examples.
The use of Bogoliubov transformations in the theories of superfluidity and superconductivity is a standard topic in quantum field theory textbooks that emphasize condensed matter applications, see for example [53]. The book [11] discusses in detail the occurrence of inequivalent representations of the commutation relations in various physical systems.
For a discussion of “Haag’s theorem”, which can be interpreted as showing that to describe an interacting quantum field theory, one must use a representation of the canonical commutation relations inequivalent to the one for free field theory, see [19].
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正文：英文 · OCR 机器稿 · 待校对
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原书 PDF · 印刷页 417、418、419、420、421、422、423、424
来源版本：2025-10-20
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