The Second quantization reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Second quantization

Second quantization refers to quantizing fieldss by expressing them in terms of creating and annihilating quanta.

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.

In the so-called "second-quantized" treatment, the treatment takes into account the quantum nature of the field in question, which is usually the light field or, in solids, the phonon field. Matter particles, too, are treated as field excitations if their number or mode changes during the evolution of the system. The entire Hamiltonian is thus written in terms of creation and annihilation operatorss. 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 the only way to accurately treat fields such as the light field.

The term is objected to by many working physicists, and is considered deprecated. 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.

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