Coherent states and bounded homogeneous domains

Monastyrsky, Michael; Perelomov, A. M.

doi:10.1016/0034-4877(74)90047-0

Cited by 20 publications

(15 citation statements)

References 12 publications

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“…If we now substitute this into (4.3) we find that on homogeneous manifolds the kinetic term (4.1) is minimized by rank one projection operators of the form |f f | where f (z) = e K(z,v) for somev, i.e. |f is a coherent state [24,29]. The associated projection operator (3.4) has symbol…”

Section: Stable Solitonsmentioning

confidence: 99%

Noncommutative solitons on Kahler manifolds

Spradlin¹,

Volovich²

2002

J. High Energy Phys.

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We construct a new class of scalar noncommutative multi-solitons on an arbitrary Kähler manifold by using Berezin's geometric approach to quantization and its generalization to deformation quantization. We analyze the stability condition which arises from the leading 1/ correction to the soliton energy and for homogeneous Kähler manifolds obtain that the stable solitons are given in terms of generalized coherent states. We apply this general formalism to a number of examples, which include the sphere, hyperbolic plane, torus and general symmetric bounded domains. As a general feature we notice that on homogeneous manifolds of positive curvature, solitons tend to attract each other, while if the curvature is negative they will repel each other. Applications of these results are discussed.

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Section: Stable Solitonsmentioning

confidence: 99%

Noncommutative solitons on Kahler manifolds

Spradlin¹,

Volovich²

2002

J. High Energy Phys.

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“…It thus appears likely that noneuclidean harmonic analysis should have many more sorts of applications, beyond those mentioned here. See, for example, the paper of Monastyrsky and Perelomov [38] and the references contained there for applications to the problem of pair creation in alternating external fields.…”

Section: Audrey Terrasmentioning

confidence: 98%

Noneuclidean Harmonic Analysis

Terras¹

1982

SIAM Rev.

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Analysis on Lie groups and their homogeneous spaces has seen a recent flowering, thanks to the work of Harish-Chandra, Helgason, Selberg and many others. The purpose of this paper is to give an elementary discussion of Fourier analysis on the noneuclidean upper half plane H; that is, the spectral resolution of the noneuclidean Laplace operator A. This leads to a study of the elementary eigenfunctions of A. Such eigenfunctions can be viewed as analogues of the trigonometric functions in euclidean Fourier analysis. The

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“…Previous results concern the hermitian symmetric spaces [2] and semisimple Lie groups which admit CS-orbits [4]. The case of the symplectic group was previously investigated in [1], [6], [5], [10], [12]. Due to lack of space we do not give here the proofs, but in general the technique is the same as in [3], where also more references are given.…”

Section: Introductionmentioning

confidence: 99%

A Holomorphic Representation of the Semidirect Sum of Symplectic and Heisenberg Lie Algebras

Berceanu¹

2012

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Coherent states and bounded homogeneous domains

Cited by 20 publications

References 12 publications

Noncommutative solitons on Kahler manifolds

Noncommutative solitons on Kahler manifolds

Noneuclidean Harmonic Analysis

A Holomorphic Representation of the Semidirect Sum of Symplectic and Heisenberg Lie Algebras

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