Prequantization, Geometric Quantization, Corrected Geometric Quantization

Abstract

A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the "salient points of the theory". The unfamiliar reader can consider this as a "soft" introduction to the topic.

Is time a cyclic dimension? Canonical quantization implicit in classical cyclic dynamics

“…This article has a mathematical character but we will use a formalism familiar to physicists. Our strategy will be the following: i) we introduce a Dirac constraint of intrinsic periodicity, first in Lagrangian form and then in Hamiltonian form [18,19], which projects ordinary Hamiltonian dynamics (non compact manifold) into related intrinsically cyclic dynamics (compact manifold); ii) we prove, by using theorems of Geometric Quantization (GQ) [1, [20][21][22][23][24], that the resulting intrinsically cyclic dynamics naturally satisfies Dirac's rules of canonical quantization -without postulating them. In short, the canonical quantization is equivalent to a local transformation from ordinary non-compact manifolds into corresponding intrinsically compact manifolds, see also [25,26].…”