Canonical Methods of Quantization

Yannick Meurice

Laure Gouba

The similarity between classical and quantum physics is large enough to make an investigation of quantization methods a worthwhile endeavour. As history has shown, Dirac's canonical quantization method works reasonably well in the case of conventional quantum mechanics over Rn but it may fail in non-trivial phase spaces and also suffer from ordering problems. Affine quantization is an alternative method, similar to the canonical quantization, that may offer a positive result in situations for which canonical quantization fails. In this paper we revisit the affine quantization method on the half-line. We formulate and solve some simple models, the free particle and the harmonic oscillator.

Ray LaPierre

Masayuki Matsuo, K. Matsuyanagi

We investigate the validity of the canonical quantization of the collective Hamiltonian derived by the selfconsistent-collective-coordinate method. Special attention is paid to the boundary condition for the (η*, η) expansion, which fixes the canonical coordinate system to carry out the quantization procedure. We remove the ambiguity of the boundary condition by requiring that the boson representations obtained by the canonical quantization agree, to the order 1/Ω, with those derived by the modified-Marumori boson-expansion method in a certain limit. Numerical examples for an exactly solvable model show that our quantization procedure provides us with remarkably accurate results.

M. Iwasaki

A canonical quantization method for the time-dependent Hartree-Fock equation is presented with the use of the generalized Hamiltonian method by Dirac.It is shown that in the Lipkin model our quantized Hamiltonian reproduces the original one approximately.