Invariance of the canonical quantization prescription under classical canonical transformations

Gin Yih Tsaur, Jyhpyng Wang

Research output: Contribution to journalArticlepeer-review

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Dirac's postulate of canonical quantization, [p̂i, q̂j] = ihδij for conjugate canonical variables, has been the most concise and general prescription on how to quantize a classical system. Since classical systems described by variables connected with canonical transformations are equivalent, [pδi, q̂j ] = ihδij must remain invariant under classical canonical transformations. This invariance has not been proved except for the limited class of cascaded infinitesimal transformations. In this paper it is shown that if (P̂i, Q̂j) are related to (p̂i, q̂j) by a classical canonical transformation, then [p̂i, q̂j] = ihδij implies [P̂i, Q̂j] = ihδij. In other words, the canonical quantization prescription is invariant for variables connected with classical canonical transformations.

Original languageEnglish
Pages (from-to)425-431
Number of pages7
JournalChinese Journal of Physics
Issue number4
StatePublished - Aug 2007


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