Generalized Coherent States and Their Applications

Perelomov, A. M.

doi:10.1007/978-3-642-61629-7

Cited by 2,826 publications

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“…with the j 0 representation being one dimensional; except for N = 2, j 0 will be the zero angular momentum state. The usual generalized coherent [6] states are defined as…”

Section: Coordinates As Coherent State Expectation Valuesmentioning

confidence: 99%

“…An extension of the concepts of integration over space and of differentiation to the present situation in which coordinates are treated as expectation values of operators in coherent states is available. The over completeness [6] of these states and the resolution of unity, µ(η; κ)d η | η; κ η; κ| = 1, with µ(η; κ) a representation dependent weight, permits the identifications 6) with N I and N D constant; N I is chosen so that, for small η,…”

Section: Jhep03(2006)040mentioning

confidence: 99%

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Coherent states and N dimensional coordinate noncommutativity

Bander

2006

J. High Energy Phys.

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Considering coordinates as operators whose measured values are expectations between generalized coherent states based on the group SO(N, 1) leads to coordinate noncommutativity together with full N dimensional rotation invariance. Through the introduction of a gauge potential this theory can additionally be made invariant under N dimensional translations. Fluctuations in coordinate measurements are determined by two scales. For small distances these fluctuations are fixed at the noncommutativity parameter while for larger distances they are proportional to the distance itself divided by a very large number. Limits on this number will lbe available from LIGO measurements.

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“…with the j 0 representation being one dimensional; except for N = 2, j 0 will be the zero angular momentum state. The usual generalized coherent [6] states are defined as…”

Section: Coordinates As Coherent State Expectation Valuesmentioning

confidence: 99%

Section: Jhep03(2006)040mentioning

confidence: 99%

Coherent states and N dimensional coordinate noncommutativity

Bander

2006

J. High Energy Phys.

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“…Following Perelomov [34], we set s = w/ √ 2j,Ĵ + = √ 2jâ † and let j → ∞. In this limit the spin coherent states transform into canonical coherent states:…”

Section: B the Limit Of Large Spinmentioning

confidence: 99%

The semiclassical coherent state propagator for systems with spin

Ribeiro¹,

Aguiar²,

Piza³

2006

J. Phys. A: Math. Gen.

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We derive the semiclassical limit of the coherent state propagator for systems with two degrees of freedom of which one degree of freedom is canonical and the other a spin. Systems in this category include those involving spin-orbit interactions and the Jaynes-Cummings model in which a single electromagnetic mode interacts with many independent two-level atoms. We construct a path integral representation for the propagator of such systems and derive its semiclassical limit.As special cases we consider separable systems, the limit of very large spins and the case of spin 1/2.

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“…H. Goldstein [1] and D. Sattinger and O. Weaver [17] have discussed the Hamiltonian from a classical viewpoint. J. Elliot and P. Dawber [7], A. Perelomov [6], and J. Klauder and E. Sudarshan [2] have examined the quantum mechanical formulation.…”

Section: The Harmonic Oscillatormentioning

confidence: 99%

“…Extensive discussion of application of Coherent States in Quantum Optics have been given by J. R. Klauder and E. C. G. Sudarshan [2] and later J. R. Klauder and B. S. Skagerstam [3], B. Wells [4], R. Cloude [5], A. Perelomov [6], and J. Elliot and P. Dawber [7].…”

Section: Introductionmentioning

confidence: 99%