Editing Correspondence principle (section)

=== Dirac's correspondence ===
[[Paul Dirac]] developed significant portions of the new quantum theory in the second half of the 1920s. While he did not apply Bohr's correspondence principle,<ref name=Darrigol_C2Q/>{{rp|308}} he developed a different, more formal classical–quantum correspondence.<ref name=Darrigol_C2Q/>{{rp|317}} Dirac connected the structures of classical mechanics known as [[Poisson brackets]] to analogous structures of quantum mechanics known as [[commutators]]:
<math display="block">\{A, B\} \longmapsto \frac{1}{i \hbar} [\hat{A}, \hat{B}].</math>
By this correspondence, now called [[canonical quantization]], Dirac showed how the mathematical form of classical mechanics could be recast as a basis for the new mathematics of quantum mechanics.

Dirac developed these connections by studying the work of Heisenberg and Kramers on dispersion, work that was directly built on Bohr's correspondence principle; the Dirac approach provides a mathematically sound path towards Bohr's goal of a connection between classical and quantum mechanics.<ref name=Darrigol_C2Q/>{{rp|348}} While Dirac did not call this correspondence a "principle", physics textbooks refer to his connections a "correspondence principle".<ref name=Messiah_vI/><!-- see Messiah index under correspondence principle -->