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, he developed a different, more formal classical–quantum correspondence. Dirac connected the structures of classical mechanics known as Poisson brackets to analogous structure of quantum mechanics known as commutators : { A , B } ⟼ ⟼ 1 i ℏ ℏ [ A ^ ^ , B ^ ^ ] . 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.