Quantic fibers for classical systems: an introduction to geometric quantization

Scientiae Studia 11 (1):35-74 (2013)
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Abstract

En este artículo, se introducirá el formalismo de cuantificación canónica denominado "cuantificación geométrica". Dado que dicho formalismo permite entender la mecánica cuántica como una extensión geométrica de la mecánica clásica, se identificarán las insuficiencias de esta última resueltas por dicha extensión. Se mostrará luego como la cuantificación geométrica permite explicar algunos de los rasgos distintivos de la mecánica cuántica, como, por ejemplo, la noconmutatividad de los operadores cuánticos y el carácter discreto de los espectros de ciertos operadores. In this article, We shall introduce the formalism of canonical quantization called "geometric quantization". Since this formalism let us understand quantum mechanics as a geometric extension of classical mechanics, we shall identify the insufficiencies of the latter that are resolved by such an extension. We shall show that geometric quantization permits us to explain some fundamental features of quantum mechanics, such as the non-commutativity of quantum operators and the discrete spectrum of some operators describing physical quantities

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Geometric foundations of classical yang–mills theory.Gabriel Catren - 2008 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 39 (3):511-531.
On Classical and Quantum Objectivity.Gabriel Catren - 2008 - Foundations of Physics 38 (5):470-487.

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