Editing Second quantization (section)

{{Use American English|date = February 2019}}
{{Short description|Formulation of the quantum many-body problem}}
{{Quantum field theory}}
'''Second quantization''', also referred to as '''occupation number representation''', is a formalism used to describe and analyze [[Quantum mechanics|quantum]] [[n-body problem|many-body]] systems. In [[quantum field theory]], it is known as [[canonical quantization]], in which the fields (typically as the [[Wave function|wave functions]] of matter) are thought of as [[field operator]]s, in a manner similar to how the physical quantities (position, momentum, etc.) are thought of as operators in [[first quantization]]. The key ideas of this method were introduced in 1927 by [[Paul Dirac]],<ref name="Dirac1927">{{cite journal
 | last = Dirac
 | first = Paul Adrien Maurice
 | title = The quantum theory of the emission and absorption of radiation
 | journal = Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character
 | volume = 114
 | number = 767
 | pages = 243–265
 | doi = 10.1098/rspa.1927.0039
 | year = 1927
 | bibcode = 1927RSPSA.114..243D
| doi-access = free
 }}</ref> and were later developed, most notably, by [[Pascual Jordan]]<ref name="Jordan1928">{{cite journal
 | last1 = Jordan
 | first1 = Pascual
 | last2 = Wigner
 | first2 = Eugene
 | title = Über das Paulische Äquivalenzverbot
 | journal = Zeitschrift für Physik
 | volume = 47
 | number = 9
 | pages = 631–651
 | doi = 10.1007/bf01331938
 | year = 1928
 | bibcode = 1928ZPhy...47..631J
 | s2cid = 126400679
 | language = de
}}</ref> and [[Vladimir Fock]].<ref name="Fock1932">{{cite journal
 | last = Fock
 | first = Vladimir Aleksandrovich
 | title = Konfigurationsraum und zweite Quantelung
 | journal = Zeitschrift für Physik
 | volume = 75
 | number = 9–10
 | pages = 622–647
 | doi = 10.1007/bf01344458
 | s2cid = 186238995
 | year = 1932
 | bibcode = 1932ZPhy...75..622F
 | language = de
}}</ref><ref name="Reed1975">{{cite book
 | last1 = Reed
 | first1 = Michael
 | author-link1 = Michael C. Reed
 | last2 = Simon
 | first2 = Barry
 | author-link2 = Barry Simon
 | title = Methods of Modern Mathematical Physics. Volume II: Fourier Analysis, Self-Adjointness
 | publisher = Academic Press
 | location = San Diego
 | year = 1975
 | pages = 328
 | isbn = 9780080925370
}}</ref>
In this approach, the quantum many-body states are represented in the [[Fock state]] basis, which are constructed by filling up each single-particle state with a certain number of identical particles.<ref name="Becchi2010">{{cite journal
 | last = Becchi
 | first = Carlo Maria
 | title = Second quantization
 | journal = Scholarpedia
 | volume = 5
 | number = 6
 | pages = 7902
 | doi = 10.4249/scholarpedia.7902
 | year = 2010
| bibcode = 2010SchpJ...5.7902B
 | doi-access = free
 }}</ref> The second quantization formalism introduces the [[creation and annihilation operators]] to construct and handle the Fock states, providing useful tools to the study of the quantum many-body theory.