second quantization

Second quantization refers to quantizing fields by expressing them as operator-valued distributions. The most elementary, or "semiclassical" treatments of quantum mechanics fix the number of particles and treat the field classically, including it as a parameter in the Hamiltonian or Lagrangian or whatever. In the so-called "second-quantized" treatment, the treatment takes into account the quantum nature of the field in question, e.g. the electromagnetic field or, in solids, the phonon field. Particles are treated as field excitations (i.e. quanta). This gives a physically informative way to treat systems in which the number of particles of a given type change with respect to time, and a way to accurately treat quantum fields. The term "second quantization" exists for historical reasons, and is considered deprecated by modern standards. This is because one is not quantizing "again", as the term "second" would suggest; one is merely shifting from a semiclassical treatment of a problem to a fully quantum-mechanical one. However, the term is still prevalent in influential older literature. There are actually different meanings of "second quantization" operators in quantum mechanics. They may increase/decrease the number of particles in the system.

Second Quantization

See also