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  1. Gabriel Catren (forthcoming). On the Relation Between Gauge and Phase Symmetries. Foundations of Physics:1-19.
    We propose a group-theoretical interpretation of the fact that the transition from classical to quantum mechanics entails a reduction in the number of observables needed to define a physical state (e.g. from \(q\) and \(p\) to \(q\) or \(p\) in the simplest case). We argue that, in analogy to gauge theories, such a reduction results from the action of a symmetry group. To do so, we propose a conceptual analysis of formal tools coming from symplectic geometry and group representation theory, (...)
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  2. Julien Page & Gabriel Catren (forthcoming). Towards a Galoisian Lnterpretation of Heisenberg Lndeterminacy Principle. Foundations of Physics:1-13.
    We revisit Heisenberg indeterminacy principle in the light of the Galois–Grothendieck theory for the case of finite abelian Galois extensions. In this restricted framework, the Galois–Grothendieck duality between finite K-algebras split by a Galois extension \(L\) and finite \(Gal(L{:}K)\) -sets can be reformulated as a Pontryagin duality between two abelian groups. We define a Galoisian quantum model in which the Heisenberg indeterminacy principle (formulated in terms of the notion of entropic indeterminacy) can be understood as a manifestation of a Galoisian (...)
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  3. Gabriel Catren (2013). Quantic Fibers for Classical Systems: An Introduction to Geometric Quantization. Scientiae Studia 11 (1):35-74.
    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, (...)
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  4. Gabriel Catren (2009). A Throw of the Quantum Dice Will Never Abolish the Copernican Revolution. Collapse: Philosophical Research and Development 5.
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  5. Gabriel Catren (2008). Geometric Foundations of Classical Yang–Mills Theory. Studies in History and Philosophy of Science Part B 39 (3):511-531.
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  6. Gabriel Catren (2008). On Classical and Quantum Objectivity. Foundations of Physics 38 (5):470-487.
    We propose a conceptual framework for understanding the relationship between observables and operators in mechanics. To do so, we introduce a postulate that establishes a correspondence between the objective properties permitting to identify physical states and the symmetry transformations that modify their gauge dependant properties. We show that the uncertainty principle results from a faithful—or equivariant—realization of this correspondence. It is a consequence of the proposed postulate that the quantum notion of objective physical states is not incomplete, but rather that (...)
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