Unternehmensnetzwerke und Virtuelle Unternehmen

Leitner, Werner; Ritsch, Karl

doi:10.1007/978-3-322-81529-3_8

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Spaces Of Almost Special Holonomy1

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“…For λ imaginary the curvature is negative and the analogue of the hyperbolic plane is anti-de Sitter space. The case λ imaginary has been recently studied in [32].…”

Section: Spaces Of Almost Special Holonomymentioning

confidence: 99%

Quantum mechanics of Yano tensors: Dirac equation in curved spacetime

Cariglia

2004

Class. Quantum Grav.

124

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In spacetimes admitting Yano tensors the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank two, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors.

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“…For λ imaginary the curvature is negative and the analogue of the hyperbolic plane is anti-de Sitter space. The case λ imaginary has been recently studied in [32].…”

Section: Spaces Of Almost Special Holonomymentioning

confidence: 99%