Generalized total angular momentum operator for the Dirac equation in curved space-time

Carter, B.; McLenaghan, R. G.

doi:10.1103/physrevd.19.1093

Cited by 271 publications

(344 citation statements)

References 18 publications

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“…Proof: The proof is given in [3] where we recover the important result of [1] derived for the Dirac field in M 4 .…”

Section: Theorem 4 the Basis Generators Of The Spinor Representationmentioning

confidence: 99%

“…In the theories with spin these operators get specific spin terms whose form is strongly dependent on the local nonholonomic frames we choose by fixing the gauge [1,2]. Recently the theory of isometries was extended allowing one to pick up well-defined conserved quantities in theories with matter fields of any spin [3,4].…”

Section: Introductionmentioning

confidence: 99%

“…The K-Y tensors play an important role in theories with spin and especially in the Dirac theory on curved spacetimes where they produce first order differential operators, called Dirac-type operators, which anticommute with the standard Dirac one, D [1,6]. Another virtue of the K-Y tensors is that they enter as square roots in the structure of several second rank S-K tensors that generate conserved quantities in classical mechanics or conserved operators which commute with D. The construction of Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Another virtue of the K-Y tensors is that they enter as square roots in the structure of several second rank S-K tensors that generate conserved quantities in classical mechanics or conserved operators which commute with D. The construction of Ref. [1] depends upon the remarkable fact that the S-K tensors must have square root in terms of K-Y tensors in order to eliminate the quantum anomaly and produce operators commuting with D [7]. These attributes of the K-Y tensors lead to an efficient mechanism of supersymmetry especially when the S-K tensor is just the metric tensor and the corresponding roots are covariantly constant K-Y tensors.…”

Section: Introductionmentioning

confidence: 99%

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Superalgebras of Dirac operators on manifolds with special Killing‐Yano tensors

Cotăescu

Visinescu²

2006

Fortschritte der Physik

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We present the properties of new Dirac-type operators generated by real or complex-valued special Killing-Yano tensors that are covariantly constant and represent roots of the metric tensor. In the real case these are just the so called complex or hyper-complex structures of the Kählerian manifolds. 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. In this way the Dirac operators are related among themselves through continuous transformations associated with specific discrete ones. We show that the group of these continuous transformations can be only U (1) or SU (2). It is pointed out that the Dirac and Dirac-type operators can form N = 4 superalgebras whose automorphisms combine isometries with the SU (2) transformation generated by the Killing-Yano tensors. As an example we study the automorphisms of the superalgebras of Dirac operators on Minkowski spacetime.Pacs 04.62.+v *

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“…Proof: The proof is given in [3] where we recover the important result of [1] derived for the Dirac field in M 4 .…”

Section: Theorem 4 the Basis Generators Of The Spinor Representationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Superalgebras of Dirac operators on manifolds with special Killing‐Yano tensors

Cotăescu

Visinescu²

2006

Fortschritte der Physik

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“…Killing-Yano (KY) tensors introduced by Yano [1] play an important role in the Dirac theory on the curved spacetimes [2]. A new supersymmetry corresponding to (KY) tensor was found in black-hole solutions of the Kerr-Newman type [3].…”

Section: Introductionmentioning

confidence: 99%

Killing-Yano Tensors and Angular Momentum

Băleanu

Defterli

2004

Czechoslovak Journal of Physics

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Superalgebra of Dirac‐type operators of the Euclidean Taub‐NUT space

Cotăescu

Visinescu

2008

Fortschritte der Physik

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The Dirac theory in the Euclidean Taub‐NUT space gives rise to a large collection of conserved operators associated to genuine or hidden symmetries. They are involved in interesting algebraic structures as dynamical algebras or even superalgebras. One presents the properties of the superalgebra of the Dirac‐type operators produced by covariantly constant Killing‐Yano tensors on the Euclidean Taub‐NUT space.

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Generalized total angular momentum operator for the Dirac equation in curved space-time

Cited by 271 publications

References 18 publications

Superalgebras of Dirac operators on manifolds with special Killing‐Yano tensors

Superalgebras of Dirac operators on manifolds with special Killing‐Yano tensors

Killing-Yano Tensors and Angular Momentum

Superalgebra of Dirac‐type operators of the Euclidean Taub‐NUT space

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