Poincaré group and relativistic wave equations in dimensions

Гитман, Д. М.; Shelepin, A. L.

doi:10.1088/0305-4470/30/17/018

Cited by 13 publications

(19 citation statements)

References 39 publications

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“…General finite representations of SO(2, 1) are classified into four types, three of which have unbounded weight spectra E 0 + n, where n ∈ Z, and the other is finite [48,[74][75][76][77]. The infinite representations are further divided into principal/supplementary series which have a bilateral unbounded weight spectrum, and highest/lowest weight series which are unbounded from above/below n = 0, respectively.…”

Section: One Solution Of This Equation Ismentioning

confidence: 99%

Horizon instability of extremal Reissner-Nordström black holes to charged perturbations

Zimmerman¹

2017

Phys. Rev. D

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We investigate the stability of highly charged Reissner-Nordström black holes to charged scalar perturbations. We show that the near-horizon region exhibits a transient instability which becomes the Aretakis instability in the extremal limit. The rates we obtain match the enhanced rates for nonaxisymmetric perturbations of the near-extremal and extremal Kerr solutions. The agreement is shown to arise from a shared near-horizon symmetry of the two scenarios.

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Section: One Solution Of This Equation Ismentioning

confidence: 99%

Horizon instability of extremal Reissner-Nordström black holes to charged perturbations

Zimmerman¹

2017

Phys. Rev. D

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“…Similar restrictions were found in [10] for the existence of a finite-dimensional covariant description. More general covariant descriptions are given in [18]. However, these are not obtained directly from the standard UIR's of the Poincaré group.…”

Section: Covariant Momentum Constraintsmentioning

confidence: 99%

“…A full classification the UIR's of the Poincaré group in 2+1 dimensions was first given by Binegar in [10], where he also discusses the possibility -and difficulties -of writing the UIR's in terms of fields on Minkowski space obeying covariant wave equations. A complete analysis of relativistic wave equations in 2+1 dimensions is given in [18] from the point of view of generalised regular representations. Our approach gives a less general treatment of the Poincaré UIR's, but maintains the link via Fourier transform between momentum space and position space.…”

Section: Introductionmentioning

confidence: 99%

Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions

Schroers¹,

Wilhelm

2014

SIGMA

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Abstract. We consider the deformation of the Poincaré group in 2+1 dimensions into the quantum double of the Lorentz group and construct Lorentz-covariant momentum-space formulations of the irreducible representations describing massive particles with spin 0, 1 2 and 1 in the deformed theory. We discuss ways of obtaining non-commutative versions of relativistic wave equations like the Klein-Gordon, Dirac and Proca equations in 2+1 dimensions by applying a suitably defined Fourier transform, and point out the relation between non-commutative Dirac equations and the exponentiated Dirac operator considered by Atiyah and Moore.

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“…Writing these constraints in a Lorentz-covariant way, and Fourier transforming leads to standard wave equations of relativistic physics like the Klein-Gordon or Dirac equation. Relativistic wave equations for anyons have also been constructed, but for spins which are not half-integers they require infinite-component wave functions, and the derivation of the equations is not straightforward [12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

“…The spin 1 equation was simply called Proca equation in[3] but it is more precisely a first order equation which implies the Proca equation. Its relation to self-dual massive field theory is discussed in[12] …”

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confidence: 99%

Non-commutative waves for gravitational anyons

Inglima

Schroers

2018

Lett Math Phys

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We revisit the representation theory of the quantum double of the universal cover of the Lorentz group in 2+1 dimensions, motivated by its role as a deformed Poincaré symmetry and symmetry algebra in (2+1)-dimensional quantum gravity. We express the unitary irreducible representations in terms of covariant, infinite-component fields on curved momentum space satisfying algebraic spin and mass constraints. Adapting and applying the method of group Fourier transforms, we obtain covariant fields on (2+1)-dimensional Minkowski space which necessarily depend on an additional internal and circular dimension. The momentum space constraints turn into differential or exponentiated differential operators, and the group Fourier transform induces a star product on Minkowski space and the internal space which is essentially a version of Rieffel's deformation quantisation via convolution. arXiv:1804.05782v2 [hep-th]

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Poincaré group and relativistic wave equations in dimensions

Cited by 13 publications

References 39 publications

Horizon instability of extremal Reissner-Nordström black holes to charged perturbations

Horizon instability of extremal Reissner-Nordström black holes to charged perturbations

Towards Non-Commutative Deformations of Relativistic Wave Equations in 2+1 Dimensions

Non-commutative waves for gravitational anyons

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