Creation and annihilation operators

Summary

Creation and annihilation operators act on the Fock space of a system of identical particles. A creation operator $a^*(f)$ adds one particle in the one-particle state $f$, and the annihilation operator $a(f)$, its adjoint, removes one. For bosons they satisfy canonical commutation relations, and for fermions the canonical anticommutation relations. Every operator of a many-particle system can be written with them, which is the language of second quantization and of quantum field theory.