36.6 For further reading
The material of this chapter is just the conventional multi-particle formalism described or implicit in most quantum field theory textbooks. Many do not explicitly discuss the non-relativistic case, two that do are [35] and [45]. Two books aimed at mathematicians that cover this subject much more comprehensively than done here are [28] and [17]. For example, section 4.5 of [28] gives a detailed description of the bosonic and fermionic Fock space constructions in terms of tensor products. For a rigorous version of the construction of annihilation and creation operators as operator-valued distributions, see for instance section 5.4 of [17], chapter X.7 of [73], or [64]. The construction of the Fock space in the infinite dimensional case using Bargmann-Fock methods of holomorphic functions (rather than tensor products) goes back to Berezin [6], and Segal (for whom it is the “complex-wave representation”, see [4]) and is explained in chapter 6 of [61].
Some good sources for learning about quantum field theory from the point of view of non-relativistic many-body theory are Feynman’s lecture notes on statistical mechanics [23], as well as [53] and [87].
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