Editing Canonical quantization (section)

{{Short description|Process of converting a classical physical theory into one compatible with quantum mechanics
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{{Quantum field theory}}{{Use American English|date=January 2019}}In [[physics]], '''canonical quantization''' is a procedure for [[quantization (physics)|quantizing]] a [[classical theory]], while attempting to preserve the formal structure, such as [[symmetry (physics)|symmetries]], of the classical theory to the greatest extent possible.

Historically, this was not quite [[Werner Heisenberg]]'s route to obtaining [[quantum mechanics]], but [[Paul Dirac]]  introduced it in his 1926 doctoral thesis, the "method of classical analogy" for quantization,<ref>{{Cite journal | last1 = Dirac | first1 = P. A. M. | title = The Fundamental Equations of Quantum Mechanics | doi = 10.1098/rspa.1925.0150 | journal = Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | volume = 109 | issue = 752 | pages = 642–653 | year = 1925 |bibcode = 1925RSPSA.109..642D | doi-access = free }}</ref>  and detailed it in his classic text ''Principles of Quantum Mechanics''.<ref name="dirac">{{cite book|last=Dirac|first=P. A. M.|author-link=Paul Dirac|title=Principles of Quantum Mechanics|publisher=Oxford University Press|location=USA|isbn=0-19-852011-5|year=1982}}</ref>  The word ''canonical'' arises from the [[Hamiltonian mechanics|Hamiltonian]] approach to classical mechanics, in which a system's dynamics is generated via canonical [[Poisson bracket]]s, a structure which is ''only partially preserved''  in canonical quantization.

This method was further used by Paul Dirac in the context of [[quantum field theory]], in his construction of [[quantum electrodynamics]].  In the field theory context, it is also called the [[second quantization]] of fields, in contrast to the semi-classical [[first quantization]] of single particles.