Supersymmetry and the geometry of Taub-NUT

Holten, J.W. van

doi:10.1016/0370-2693(94)01358-j

Cited by 76 publications

(91 citation statements)

References 20 publications

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“…The latter is characterized by the supercharge anticommuting for the nonlinear operator different from the Hamiltonian and equal to the (shifted for the constant) square of the total angular momentum operator. The nonlinear supersymmetry of the similar form was observed also under investigation of the space-time symmetries in terms of the motion of pseudoclassical spinning point particles [3,4,5], and was revealed in the 3D P, T -invariant systems of relativistic fermions [6] and Chern-Simons fields [7]. In this letter we show that the generators of the nonstandard [1] and standard [2] supersymmetries have to be supplemented by their product operator to be treated as independent supercharge.…”

supporting

confidence: 60%

On the nature of fermion-monopole supersymmetry

Plyushchay

2000

Physics Letters B

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It is shown that the generator of the nonstandard fermion-monopole supersymmetry uncovered by De Jonghe, Macfarlane, Peeters and van Holten, and the generator of its standard N = 1/2 supersymmetry have to be supplemented by their product operator to be treated as independent supercharge. As a result, the fermion-monopole system possesses the nonlinear N = 3/2 supersymmetry having the nature of the 3D spin-1/2 free particle's supersymmetry generated by the supercharges represented in a scalar form. Analyzing the supercharges' structure, we trace how under reduction of the fermion-monopole system to the spherical geometry the nonlinear N = 3/2 superalgebra comprising the Hamiltonian and the total angular momentum as even generators is transformed into the standard linear N = 1 superalgebra with the Hamiltonian to be the unique even generator. *

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confidence: 60%

On the nature of fermion-monopole supersymmetry

Plyushchay

2000

Physics Letters B

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“…There are four Killing-Yano tensors in the usual, locally isotropic, Taub-NUT geometry [27] which for anisotropic spaces are transformed into corresponding d-tensors for anisotropic Taub-NUT spaces, [28], in our case distinguished by the N -connection structure [16]: Starting with these results from the bosonic sector of the Taub-NUT space one can proceed with the spin contributions. The first generalized Killing equation (49) shows that with each Killing vector R µ A there is an associated Killing scalar B A .…”

Section: Anisotropic Taub-nut Spinning Spacementioning

confidence: 99%

“…The expression for the Killing scalar is taken as in Ref. [28]: [µ;ν] ψ µ ψ ν with that modification that we use a d-covariant derivation which gives that the total angular momentum and "relative electric charge" become in the anisotropic spinning case The non-vanishing Poisson brackets are (after some algebra):…”

Section: Anisotropic Taub-nut Spinning Spacementioning

confidence: 99%

Anholonomic frames, generalized Killing equations, and anisotropic Taub-NUT spinning spaces

2002

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By using anholonomic frames in (pseudo)-Riemannian spaces we define anisotropic extensions of Euclidean Taub-NUT spaces. With respect to coordinate frames such spaces are described by offdiagonal metrics which could be diagonalized by corresponding anholonomic transforms. We define the conditions when the 5D vacuum Einstein equations have as solutions anisotropic Taub-NUT spaces. The generalized Killing equations for the configuration space of anisotropically spinning particles (anisotropic spinning space) are analyzed. Simple solutions of the homogeneous part of these equations are expressed in terms of some anisotropically modified Killing-Yano tensors. The general results are applied to the case of the four-dimensional locally anisotropic Taub-NUT manifold with Euclidean signature. We emphasize that all constructions are for (pseudo)-Riemannian spaces defined by vacuum solutions, with generic anisotropy, of 5D Einstein equations, the solutions being generated by applying the moving frame method. 

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“…The antisymmetric tensor S µν = −iθ µ θ ν generates the internal part of the local tangent space rotations. For example, in the spinning Euclidean Taub-NUT space such operators correspond to components of the spin which are separately conserved [17].…”

Section: Discussionmentioning

confidence: 99%

Symmetries of the Dirac operators associated with covariantly constant Killing–Yano tensors

Cotăescu

Visinescu

2003

Class. Quantum Grav.

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The continuous and discrete symmetries of the Dirac-type operators produced by particular Killing-Yano tensors are studied in manifolds of arbitrary dimensions. The Killing-Yano tensors considered are covariantly constant and realize certain square roots of the metric tensor. Such a Killing-Yano tensor produces simultaneously a Dirac-type operator and the generator of a one-parameter Lie group connecting this operator with the standard Dirac one. The Dirac operators are related among themselves through continuous or discrete transformations. It is shown that the groups of the continuous symmetry can be only U (1) and SU (2), specific to (hyper-)Kähler spaces, but arising even in cases when the requirements for these special geometries are not fulfilled. The discrete symmetries are also studied obtaining the discrete groups Z 4 and Q. The briefly presented examples are the Euclidean Taub-NUT space and the Minkowski spacetime.Pacs 04.62.+v

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Supersymmetry and the geometry of Taub-NUT

Cited by 76 publications

References 20 publications

On the nature of fermion-monopole supersymmetry

On the nature of fermion-monopole supersymmetry

Anholonomic frames, generalized Killing equations, and anisotropic Taub-NUT spinning spaces

Symmetries of the Dirac operators associated with covariantly constant Killing–Yano tensors

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