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Souriau, Jean-Marie

doi:10.1007/978-1-4612-0281-3_9

Cited by 19 publications

(48 citation statements)

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“…We mention for completeness that the Lagrangians (2.2) are the Cartan forms of the Souriau forms [14,28],…”

Section: Chiral Oscillatorsmentioning

confidence: 99%

“…The possibility of decomposing an isolated system into center-of-mass and relative coordinates has been linked to Galilean symmetry : Souriau [14] argued, in fact, that this property depends on the Galilei group having an invariant Abelian subgroup -namely the one spanned by translations and (Galilean) boosts.…”

mentioning

confidence: 99%

“…Remarkably, the cohomological structure which determines the existence of a central extension originates precisely in this subgroup [14,15]. Remember that, in dimension d ≥ 3, both the Newton-Hooke and the Galilei groups have a one-parameter central extension, but in the plane they both admit an "exotic", two-parameter central extension [16][17][18][19].…”

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confidence: 99%

“…The proof will be accomplished by applying the orbit method, which provides us indeed with all systems upon which the symmetry group acts transitively [14,[20][21][22].…”

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confidence: 99%

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Newton–Hooke-type symmetry of anisotropic oscillators

Zhang¹,

Horváthy²,

Andrzejewski³

et al. 2013

Annals of Physics

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The rotation-less Newton-Hooke -type symmetry found recently in the Hill problem and instrumental for explaining the center-of-mass decomposition is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton-Hooke symmetry is recovered in the isotropic case.Star escape from a Galaxy is studied as application.

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“…We mention for completeness that the Lagrangians (2.2) are the Cartan forms of the Souriau forms [14,28],…”

Section: Chiral Oscillatorsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

“…The proof will be accomplished by applying the orbit method, which provides us indeed with all systems upon which the symmetry group acts transitively [14,[20][21][22].…”

mentioning

confidence: 99%

See 2 more Smart Citations

Newton–Hooke-type symmetry of anisotropic oscillators

Zhang¹,

Horváthy²,

Andrzejewski³

et al. 2013

Annals of Physics

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“…Symplectic manifolds have a very rich geometric structure, that allows us to reproduce many classic quantum mechanical results that seem to need a priori the notion of the Hilbert space. Such is the case for Wigner's classification of particles (from the geometric quantisation of Konstant-Souriau [32]) and many aspects of the spin-statistics relation [33].…”

Section: Phases As Primitive Ingredientsmentioning

confidence: 99%

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Anastopoulos

2003

International Journal of Theoretical Physics

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We argue that the complex numbers are an irreducible object of quantum probability: this can be seen in the measurements of geometric phases that have no classical probabilistic analogue. Having the complex phases as primitive ingredient implies that we need to accept non-additive probabilities. This has the desirable consequence of removing constraints of standard theorems about the possibility of describing quantum theory with commutative variables. Motivated by the formalism of consistent histories and keeping an analogy with the theory of stochastic processes, we develop a (statistical) theory of quantum processes: they are characterised by the introduction of a "density matrix" on phase space paths (it thus includes phase information) and fully reproduces quantum mechanical predictions. We can write quantum differential equations (in analogy to Langevin equation) that could be interpreted as referring to individual quantum systems. We describe the reconstruction theorem by which a quantum process can yield the standard Hilbert space structure if the Markov property is imposed. We discuss the relevance of our results for the interpretation of quantum theory (a sample space is possible if probabilities are non-additive) and quantum gravity (the Hilbert space arises here after the consideration of a background causal structure).

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Can Classical Description of Physical Reality Be Considered Complete?

Catren

2009

The Western Ontario Series in Philosophy of Science

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Abstract. We propose a definition of physical objects that aims to clarify some interpretational problems in quantum mechanics. We claim that the transformations induced by an objective property of a physical system must leave invariant all the other objective properties of the same system. The uncertainty principle is understood as a natural consequence of the imbrication between objective properties and non-objective properties. It follows from the proposed definition that in classical mechanics non-objective properties are wrongly considered objective. We conclude that, unlike classical mechanics, quantum mechanics provides a complete objective description of physical systems.

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Cited by 19 publications

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Newton–Hooke-type symmetry of anisotropic oscillators

Newton–Hooke-type symmetry of anisotropic oscillators

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Can Classical Description of Physical Reality Be Considered Complete?

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