Geometric foundations of classical Yang–Mills theory

Catren, Gabriel

doi:10.1016/j.shpsb.2008.02.002

Cited by 17 publications

(18 citation statements)

References 21 publications

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“…v p ) associated to the objective property in question. 13 We can thus conclude that phase space is not an adequate geometric arena for defining physical systems that satisfy the phase postulate. It is worth stressing that this conceptual justification of the reduction in the number of variables that are necessary to completely decribe a physical system does not presuppose any kind of epistemic restriction to the amount of information an observer can have about an object.…”

Section: Phase Postulatementioning

confidence: 96%

Quantum Ontology in the Light of Gauge Theories

Catren

2014

Probing the Meaning of Quantum Mechanics

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We propose the conjecture according to which the fact that quantum mechanics does not admit sharp value attributions to both members of a complementary pair of observables can be understood in the light of the symplectic reduction of phase space in constrained Hamiltonian systems. In order to unpack this claim, we propose a quantum ontology based on two independent postulates, namely the phase postulate and the quantum postulate. The phase postulate generalizes the gauge correspondence between first-class constraints and gauge transformations to the observables of unconstrained Hamiltonian systems. The quantum postulate specifies the relationship between the numerical values of the observables that permit us to individualize a physical system and the symmetry transformations generated by the operators associated to these observables. We argue that the quantum postulate and the phase postulate are formally implemented by the two independent stages of the geometric quantization of a symplectic manifold, namely the prequantization formalism and the election of a polarization of pre-quantum states respectively.

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Section: Phase Postulatementioning

confidence: 96%

Quantum Ontology in the Light of Gauge Theories

Catren

2014

Probing the Meaning of Quantum Mechanics

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“…the transformations of the frames in P that do not depend on m ∈ M (see Ref. [7] and references therein). As we have just shown, this localization of the global gauge transformations can be understood in terms of the passage from the usual "global" h-action on the H-principal bundle P → M to the "localized" action defined by the sections of the adjoint algebroid P ×H h → M .…”

Section: Vertical Parallelism and Ehresmann Connectionsmentioning

confidence: 99%

Geometric foundations of Cartan gauge gravity

Catren

2015

Int. J. Geom. Methods Mod. Phys.

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Abstract. We use the theory of Cartan connections to analyze the geometrical structures underpinning the gauge-theoretical descriptions of the gravitational interaction. According to the theory of Cartan connections, the spin connection ω and the soldering form θ that define the fundamental variables of the Palatini formulation of general relativity can be understood as different components of a single field, namely a Cartan connection A = ω + θ. In order to stress both the similarities and the differences between the notions of Ehresmann connection and Cartan connection, we explain in detail how a Cartan geometry (PH → M, A) can be obtained from a G-principal bundle PG → M endowed with an Ehresmann connection (being the Lorentz group H a subgroup of G) by means of a bundle reduction mechanism. We claim that this reduction must be understood as a partial gauge fixing of the local gauge symmetries of PG, i.e. as a gauge fixing that leaves "unbroken" the local Lorentz invariance. We then argue that the "broken" part of the symmetry-that is the internal local translational invariance-is implicitly preserved by the invariance under the external diffeomorphisms of M.

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“…En otro lugar (Catren, en prensa), propongo una interpretación de la cuantificación geométrica que permite entender la necesidad de polarizar los estados precuánticos a partir de un principio físico proveniente de las teorías de gauge (o teorías hamiltonianas con vínculos), a saber la existencia de una correspondencia entre los vínculos de primera clase y las transformaciones de gauge (cf. Catren, 2008a;2009).…”

Section: Introductionunclassified

Fibras cuánticas para sistemas clásicos: introducción a la cuantificación geométrica

Catren¹

2013

Sci. stud.

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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.

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Geometric foundations of classical Yang–Mills theory

Cited by 17 publications

References 21 publications

Quantum Ontology in the Light of Gauge Theories

Quantum Ontology in the Light of Gauge Theories

Geometric foundations of Cartan gauge gravity

Fibras cuánticas para sistemas clásicos: introducción a la cuantificación geométrica

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