Canonical quantization

In <a href="/facts/Physics/a7aH2y08">physics</a>, canonical quantization is a procedure for <a href="/facts/Quantization_(physics)/fvs2Jwpn">quantizing</a> a <a href="/facts/Classical_theory/gGnINVPE">classical theory</a>, while attempting to preserve the formal structure, such as <a href="/facts/Symmetry_(physics)/gJmgsooI">symmetries</a>, of the classical theory to the greatest extent possible.
Historically, this was not quite <a href="/facts/Werner_Heisenberg/n4qzYvj4">Werner Heisenberg</a>'s route to obtaining <a href="/facts/Quantum_mechanics/BRc3Mzgr">quantum mechanics</a>, but <a href="/facts/Paul_Dirac/6bt5yRdk">Paul Dirac</a> introduced it in his 1926 doctoral thesis, the "method of classical analogy" for quantization, and detailed it in his classic text Principles of Quantum Mechanics. The word canonical arises from the <a href="/facts/Hamiltonian_mechanics/2ReerlNA">Hamiltonian</a> approach to classical mechanics, in which a system's dynamics is generated via canonical <a href="/facts/Poisson_bracket/7WUH7VXV">Poisson brackets</a>, a structure which is only partially preserved in canonical quantization.
This method was further used by Paul Dirac in the context of <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theory</a>, in his construction of <a href="/facts/Quantum_electrodynamics/zPteAr6G">quantum electrodynamics</a>. In the field theory context, it is also called the <a href="/facts/Second_quantization/PPJHwX1Q">second quantization</a> of fields, in contrast to the semi-classical <a href="/facts/First_quantization/ASAseqAW">first quantization</a> of single particles.

Canonical quantization open-in-new

Canonical quantization