Generalized coherent states for spinning relativistic particles

Anastopoulos, Charis

doi:10.1088/0305-4470/37/36/004

Cited by 3 publications

(3 citation statements)

References 32 publications

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“…The above suggests a naturally defined Fubinitype metric on the phase space [68][69][70][71][72][73][74][75][76][77][78]…”

Section: Phase Space Quantizationmentioning

confidence: 99%

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Phase space holography with no strings attached

Khveshchenko¹

2022

physics

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Keywords: phase space, holographic correspondence, hydrodynamics, effective metric We discuss the Wigner function representation from the novel standpoint of establishing a natural holographylike correspondence between the descriptions of a generic quantum system in the phase space (‘bulk’) picture versus its spacetime (‘boundary’) counterpart. In certain cases, the former may reduce to the gravity-like dynamics of a local metric-type variable while the latter takes on the form of some bosonized collective field hydrodynamics. This generic pseudo-holographic duality neither relies on any particular symmetry of the system in question, nor does it require any relation to some underlying ‘string theory’, thus providing a systematic way of constructing practical – as opposed to the previous ‘ad hoc’ – examples of genuine holographic duality.

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“…The above suggests a naturally defined Fubinitype metric on the phase space [68][69][70][71][72][73][74][75][76][77][78]…”

Section: Phase Space Quantizationmentioning

confidence: 99%

“…It is well known that the non-linear hydrodynamic Eqs. ( 21) and (22) can even be derived from the Schroedinger equation for a free particle of mass m [68][69][70][71][72][73][74][75][76][77][78]. Specifically, by applying the Madelung parameterization of the wave function…”

Section: Non-linear Hydrodynamicsmentioning

confidence: 99%

Phase space holography with no strings attached

Khveshchenko¹

2022

physics

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“…An extensive bibliography (up to early 21st century) was given in the review [10]. Only in the last few months there appeared a number of interesting works devoted to generalization of vector coherent states for the case of matrix index ( [11]- [14]), hypergeometric [15] and combinatorial [16] coherent states,as well as to further development of mathematical [17,18] and physical [19,20] applications of coherent states, including applications to the description of models with exactly solvable potentials [21], super-symmetric conformal field theory [22] and to path integral [23] in holomorphic representation.…”

Section: Introductionmentioning

confidence: 99%

Generalized coherent states for q-oscillator connected with q-Hermite polynomials

Borzov

2003

International Seminar Day on Diffraction, 2003. Proceedings.

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For the oscillator-like systems, connected with q-Hermite polynomials, coherent states of Barut-Girardello type are defined. The well-known Arik-Coon oscillator naturally arose in the framework of suggested approach as oscillator, connected with the Rogers q-Hermite polynomials, in the same way as usual oscillator with standard Hermite polynomials. The results about the coherent states for discrete q-Hermite polynomials of II type are quite new.

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Glafka 2004: Some Remarks on the Role of Complex Numbers in Quantum Theory

Anastopoulos

2006

Int J Theor Phys

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We consider the issue of whether complex numbers are necessary in the formulation of quantum theory. We argue that their introduction is not forced on us by the dynamics, but it is absolutely necessary in order to incorporate the observable properties of the geometric phases that appear in interference experiments. This remark provides the motivation for the construction of a histories-based axiomatic scheme for quantum theory, in which phases are considered as primitive elements, on equal footing with probabilities. This scheme reduces to standard quantum theory for systems characterised by a background causal structure-however it may lead to a different description in the domain of quantum gravity.

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Generalized coherent states for spinning relativistic particles

Cited by 3 publications

References 32 publications

Phase space holography with no strings attached

Phase space holography with no strings attached

Generalized coherent states for q-oscillator connected with q-Hermite polynomials

Glafka 2004: Some Remarks on the Role of Complex Numbers in Quantum Theory

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