Fermion on Curved Spaces, Symmetries, and Quantum Anomalies

Visinescu, Mihai

doi:10.3842/sigma.2006.083

Cited by 4 publications

(5 citation statements)

References 42 publications

(113 reference statements)

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“…In the present two short-wave components case, this corresponds to |Φ| → ∞, which is possible for either |N | 2 = 0 or |D 1 | 2 = 0. But a careful analysis of the expression (23) along with a consideration of the non-singularity condition (19) into account shows that both |N | 2 and |D 1 | 2 are positive definite which ensures that |Φ| is always a finite quantity. Thus it seems that the present solution does not admit the soliton resonance phenomenon.…”

Section: A Two Short-wave Components Casementioning

confidence: 99%

“…Very recently, the non-integrable three component Gross-Pitaevskii equations have been reduced to single component Yajima-Oikawa system by using multiple scale method [18]. In another recent work [19], the one-dimensional integrable two-component Zakharov-Yajima-Oikawa equation has been derived using multiple scale method and special bright-dark one-soliton solutions have been reported.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, much attention has been paid to investigate mixed (bright-dark) soliton dynamics in different dynamical systems including nonlinear optical systems and Bose-Einstein condensates [1,8,14,18,19,[25][26][27] of coupled bright-dark solitons and to analyse their propagation properties and collision dynamics. In the present work, we derive the (2+1)-dimensional N -component LSRI system governing the evolution of m short-waves and n longwaves (with m + n = N ) in a nonlinear dispersive medium and reduce the system to an integrable system for a particular choice of the system parameters.…”

Section: Introductionmentioning

confidence: 99%

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Mixed solitons in a (2+1)-dimensional multicomponent long-wave–short-wave system

Kanna¹,

Vijayajayanthi

Lakshmanan

2014

Phys. Rev. E

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We derive a (2+1)-dimensional multicomponent long-wave-short-wave resonance interaction (LSRI) system as the evolution equation for propagation of N-dispersive waves in weak Kerr-type nonlinear medium in the small-amplitude limit. The mixed- (bright-dark) type soliton solutions of a particular (2+1)-dimensional multicomponent LSRI system, deduced from the general multicomponent higher-dimensional LSRI system, are obtained by applying the Hirota's bilinearization method. Particularly, we show that the solitons in the LSRI system with two short-wave components behave like scalar solitons. We point out that for an N-component LSRI system with N>3, if the bright solitons appear in at least two components, interesting collision behavior takes place, resulting in energy exchange among the bright solitons. However, the dark solitons undergo standard elastic collision accompanied by a position shift and a phase shift. Our analysis on the mixed bound solitons shows that the additional degree of freedom which arises due to the higher-dimensional nature of the system results in a wide range of parameters for which the soliton collision can take place.

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Section: A Two Short-wave Components Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mixed solitons in a (2+1)-dimensional multicomponent long-wave–short-wave system

Kanna¹,

Vijayajayanthi

Lakshmanan

2014

Phys. Rev. E

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“…Here ω n is the wedge product of ω with itself n times. The volume of a Kähler manifold can also be written as [10,11]…”

Section: Toric Sasaki-einstein Spacesmentioning

confidence: 99%

Complete integrability of geodesic motion in Sasaki–Einstein toric Yp,q spaces

Babalic¹,

Visinescu²

2015

Mod. Phys. Lett. A

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We construct explicitly the constants of motion for geodesics in the 5-dimensional Sasaki-Einstein spaces Y p,q . To carry out this task we use the knowledge of the complete set of Killing vectors and Killing-Yano tensors on these spaces. In spite of the fact that we generate a multitude of constants of motion, only five of them are functionally independent implying the complete integrability of geodesic flow on Y p,q spaces. In the particular case of the homogeneous Sasaki-Einstein manifold T 1,1 the integrals of motion have simpler forms and the relations between them are described in detail.

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“…At this time, the evaluation of the commutator between H and the quantum operators, eq. ( 19), is more involved and the result of this tedious evaluation is [13,14] […”

Section: -P2mentioning

confidence: 99%

Hidden conformal symmetries and quantum-gravitational anomalies

Visinescu¹

2010

EPL

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The relationship between conformal symmetries in a curved-space background and the corresponding quantum operators that commute with the fundamental wave operator in a firstquantized field theory is investigated. It is shown that the conformal Killing vectors and tensors do not in general produce symmetry operators for the Klein-Gordon equation. These differ from the standard Killing tensors for which, under a few notable favorable circumstances, the existence of such operators is possible.

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Fermion on Curved Spaces, Symmetries, and Quantum Anomalies

Cited by 4 publications

References 42 publications

Mixed solitons in a (2+1)-dimensional multicomponent long-wave–short-wave system

Mixed solitons in a (2+1)-dimensional multicomponent long-wave–short-wave system

Complete integrability of geodesic motion in Sasaki–Einstein toric Yp,q spaces

Hidden conformal symmetries and quantum-gravitational anomalies

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