The moyal representation for spin

Várilly, Joseph C.; Gracia‐Bondía, José M.

doi:10.1016/0003-4916(89)90262-5

Cited by 277 publications

(338 citation statements)

References 27 publications

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“…[46,47]). One practical and formally justified [48,49] axiomatic basis for algorithm (II) postulates the equations of motion for averages of certain physical quantities [38,50].…”

Section: The Fundamentals Of Generalized Wigner Representationsmentioning

confidence: 99%

Wigner representation of the rotational dynamics of rigid tops

Zhdanov

Seideman

2015

Phys. Rev. A

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“…[46,47]). One practical and formally justified [48,49] axiomatic basis for algorithm (II) postulates the equations of motion for averages of certain physical quantities [38,50].…”

Section: The Fundamentals Of Generalized Wigner Representationsmentioning

confidence: 99%

Wigner representation of the rotational dynamics of rigid tops

Zhdanov

Seideman

2015

Phys. Rev. A

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“…Faure and Zhilinskii use the pre-factor 1 j , instead of 2 dj , in front of the coupling term J · S. But, the factor 1 dj turns out to be the expansion parameter of the -product to be introduced in this context 29,30,49 , and is therefore better suited for our purposes 50 . Anyway, in the (adiabatic) limit j → ∞, the difference of the two factors becomes negligible.…”

Section: A Model With Non-commutative Slow Variables: Spin-orbit mentioning

confidence: 99%

“…In principle, we can also define a Berezin--product for a spin coherent state quantisation of the scale of Poisson algebras C ∞ (S 2 ) = dj ∈N C ∞ dj (S 2 ), because a closed de-quantisation formula, similar to (4.3), exists 30,42 . A d j -expansion of this -product is arrived at via an easy, but extremely tedious, calculation along the lines of 49 .…”

Section: Remark Iv1mentioning

confidence: 99%

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

Stottmeister

Thiemann

2016

Journal of Mathematical Physics

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This article, as the first of three, aims at establishing the (time-dependent) BornOppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework, and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g. spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article, and its companion, affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).

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“…takes values in the hermitian 2 × 2 matrices, see [VGB89]. The quantisers ∆ 1/2 (n) provide a quantum-classical correspondence on the sphere that is covariant with respect to SU(2)-rotations in the following sense,…”

Section: Classical Limit Of Quantum Dynamicsmentioning

confidence: 99%

Zitterbewegung and semiclassical observables for the Dirac equation

Bölte¹,

Glaser²

2004

J. Phys. A: Math. Gen.

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In a semiclassical context we investigate the Zitterbewegung of relativistic particles with spin 1/2 moving in external fields. It is shown that the analogue of Zitterbewegung for general observables can be removed to arbitrary order in by projecting to dynamically almost invariant subspaces of the quantum mechanical Hilbert space which are associated with particles and anti-particles. This not only allows to identify observables with a semiclassical meaning, but also to recover combined classical dynamics for the translational and spin degrees of freedom. Finally, we discuss properties of eigenspinors of a Dirac-Hamiltonian when these are projected to the almost invariant subspaces, including the phenomenon of quantum ergodicity.

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The moyal representation for spin

Cited by 277 publications

References 27 publications

Wigner representation of the rotational dynamics of rigid tops

Wigner representation of the rotational dynamics of rigid tops

Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations

Zitterbewegung and semiclassical observables for the Dirac equation

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