4 Second quantization
To solve many-particle problems, it is expedient to introduce the language of second quantization. This approach does not add new conceptual baggage to quantum mechanics. Rather, it provides a convenient book-keeping method for dealing with many-particle states. As a result, we will be brief in the formal development of this technique. For a more complete development, see, for example, Baym (B1969). We develop this approach for fermions, that is, particles that are antisymmetric with respect to interchange of any two of their coordinates, and for bosons, particles for which such interchanges do not incur any sign change in the many-particle wavefunction.
Consider the many-body state of a boson system containing ...