Mathematical, Theoretical and Phenomenological Challenges Beyond the Standard Model 2005
DOI: 10.1142/9789812702166_0017
|View full text |Cite
|
Sign up to set email alerts
|

Symmetries and Supersymmetries of the Dirac-Type Operators on Euclidean Taub-Nut Space

Abstract: It is shown that the main geometrical objects involved in all the symmetries or supersymmetries of the Dirac operators in curved manifolds of arbitrary dimensions are the Killing vectors and the Killing-Yano tensors of any ranks. The general theory of external symmetry transformations associated to the usual isometries is presented, pointing out that these leave the standard Dirac equation invariant providing the correct spin parts of the group generators. Furthermore, one analyzes the new type of symmetries g… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1

Citation Types

0
25
0

Year Published

2005
2005
2010
2010

Publication Types

Select...
6

Relationship

1
5

Authors

Journals

citations
Cited by 9 publications
(25 citation statements)
references
References 57 publications
0
25
0
Order By: Relevance
“…Recently we have shown that the symmetries of this type can not be larger than SU(2) [11]. Moreover, we pointed out that their transformations can be mixed with the isometries in order to obtain the automorphisms of the superalgebras of Dirac and Dirac-type operators of the hyper-Kähler manifolds [13]. In the present paper we continue this study focusing on the automorphisms of the superalgebras of Dirac operators on non-Kählerian manifolds, including the Minkowski spacetime.…”
Section: Introductionmentioning
confidence: 79%
See 1 more Smart Citation
“…Recently we have shown that the symmetries of this type can not be larger than SU(2) [11]. Moreover, we pointed out that their transformations can be mixed with the isometries in order to obtain the automorphisms of the superalgebras of Dirac and Dirac-type operators of the hyper-Kähler manifolds [13]. In the present paper we continue this study focusing on the automorphisms of the superalgebras of Dirac operators on non-Kählerian manifolds, including the Minkowski spacetime.…”
Section: Introductionmentioning
confidence: 79%
“…It is obvious that Eq. (4) gives just the canonical commutation rules of a Lie algebra isomorphic with that of the groups G(η) or G(η) [11,13]. The spinor and vector representations are related between themselves through the following Theorem 1 For any real or complex valued skew-symmetric tensor ωαβ = −ωβα the matrix…”
Section: Definitionmentioning
confidence: 99%
“…A typical example is the four-dimensional Euclidean Taub-NUT space which involves the potentials of the Dirac magnetic monopole and satisfies the vacuum Einstein equations. Moreover, this geometry is hiper-Kähler having many interesting properties related to a specific hidden symmetry [11]. For this reason the Kählerian geometries were considered for generalizing the Dirac monopole to many dimensions [4].…”
Section: Introductionmentioning
confidence: 99%
“…Moreover, this space is hiper-Kähler having many interesting properties related to a specific hidden symmetry [6,7]. For this reason the Kählerian geometries were considered for generalizing the Dirac monopole to many dimensions [8].…”
mentioning
confidence: 99%
“…Next let us consider the motion of a test particle in the gravitational and magnetic fields of a massive Dirac monopole at large distances. We suppose that the test particle is a quantum scalar particle of the bare mass m and charge e = q/µ ef where q is the eigenvalue of the operator Q = −i∂ α [7]. The scalar field Φ of the test particle obeys the five-dimensional Klein-Gordon equation ( − m 2 )Φ = 0 [11].…”
mentioning
confidence: 99%