Conformal properties of Chern-Simons vortices in external fields

Duval, Christian; Horváthy, P. A.; Palla, L.

doi:10.1103/physrevd.50.6658

Cited by 57 publications

(96 citation statements)

References 19 publications

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“…Note, however, that the coupling constant here is the mass, m, not the electric charge. Consistently with [6,8], the SL(2, R) survives the inclusion of a Dirac monopole [39], or of an AharonovBohm vector potential into the components of the metric (6) [4,28].…”

Section: The Equivalence Principlementioning

confidence: 99%

“…As seen before, a non-relativistic conformal transformation acts on (M ,ḡ µν ) by isometries. Implementing them according to (28) yields, once again, symmetries. Does we have more conformal transformations than just the mere isometries ?…”

Section: Properties Of the Metric (2)mentioning

confidence: 99%

“…The metric (39) is that of AdS as it should, since the function in front of dt 2 trivially satisfies (5). The simplest way to understand the origin of NewtonHooke symmetries is to realize that they are, in fact, "imported" Galilean symmetries [9,28,30,31,32]. Putting ω = τ −2 , the time-dependent dilatation,…”

Section: Conformal Extension Of the Newton-hooke Groupmentioning

confidence: 99%

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The geometry of Schrödinger symmetry in non-relativistic CFT

Duval¹,

Horváthy²

2009

Annals of Physics

Self Cite

127

132

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The non-relativistic conformal "Schrödinger" symmetry of some gravity backgrounds proposed recently in the AdS/CFT context, is explained in the "Bargmann framework". The formalism incorporates the Equivalence Principle. Newton-Hooke conformal symmetries, which are analogs of those of Schrödinger in the presence of a negative cosmological constant, are discussed in a similar way. Further examples include topologically massive gravity with negative cosmological constant and the Madelung hydrodynamical description.

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Section: The Equivalence Principlementioning

confidence: 99%

Section: Properties Of the Metric (2)mentioning

confidence: 99%

Section: Conformal Extension Of the Newton-hooke Groupmentioning

confidence: 99%

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The geometry of Schrödinger symmetry in non-relativistic CFT

Duval¹,

Horváthy²

2009

Annals of Physics

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127

132

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“…For the harmonic oscillator, for example, every half-period can be conformally related to a full free motion. Then the Maslov correction can be recovered by fitting together the wave function at half-periods [41,42]. This latter paper also provides a complete catalog of all possibilities.…”

Section: Resultsmentioning

confidence: 99%

“…Related questions are also discussed in some textbooks [9,35,36]. It is worth calling the attention to that all path integrals studied in this paper can be calculated [37][38][39] by transforming the system into the free form using a "nonrelativistic conformal transformation" [40][41][42]. For the harmonic oscillator, for example, every half-period can be conformally related to a full free motion.…”

Section: Resultsmentioning

confidence: 99%

The Maslov correction in the semiclassical Feynman integral

Horváthy

2010

Open Physics

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Abstract:The Maslov correction to the wave function is the jump of (− π 2 ) in the phase when the system passes through a caustic. This can be explained by studying the second variation and the geometry of paths, as conveniently seen in Feynman's path integral framework. The results can be extended to any system using the semiclassical approximation. The 1-dimensional harmonic oscillator is used to illustrate the different derivations reviewed here.

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The gravitational field of a light wave

Holten

2010

Fortschritte der Physik

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According to the classical Einstein-Maxwell theory of gravity and electromagnetism, a light-wave traveling in empty space-time is accompanied by a gravitational field of the pp-type. Therefore point masses are scattered by a light wave, even if they carry no electric or magnetic charge, or dipole moment. In this paper I present the explicit form of the metric and curvature for both circularly and linearly polarized light, and discuss the geodesic motion of test masses. This is followed by a discussion of classical scattering of point particles by the gravitational field associated with a circularly polarized electromagnetic block wave. A generalization to a quantum theory of particles in the background of these classical wave fields is presented in terms of the covariant Klein-Gordon equation. I derive the energy spectrum of quantum particles in the specific case of the circularly polarized block wave. Finally, a few general remarks on the extension to a quantum light wave are presented.Comment: 15 pages, 2 figure

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Conformal properties of Chern-Simons vortices in external fields

Cited by 57 publications

References 19 publications

The geometry of Schrödinger symmetry in non-relativistic CFT

The geometry of Schrödinger symmetry in non-relativistic CFT

The Maslov correction in the semiclassical Feynman integral

The gravitational field of a light wave

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