Invariance of the Canonical Quantization Prescription under Classical Canonical Transformations

Gin-Yih Tsaur ； Jyhpyng Wang

《Chinese Journal of Physics》 45卷4期 (2007/08) Pp. 425-431

並列摘要

Dirac's postulate of canonical quantization, [(The Symbol is abbreviated)]=-iħδ(subscript ij) 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, [(The Symbol is abbreviated)]=-iħδ(subscript ij) 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 ((The Symbol is abbreviated)) are related to ((The Symbol is abbreviated)) by a classical canonical transformation, then [(The Symbol is abbreviated)]=-iħδ(subscript ij) In other words, the canonical quantization prescription is invariant for variables connected with classical canonical transformations.