Killing spinor Guide, Meaning , Facts, Information and Description

Killing spinor is a term used in mathematics and physics. By the more narrow definition, commonly used in mathematics, the term Killing spinor indicates those twistor spinors which are also eigenspinors of the Dirac operator.

Another equivalent definition is that Killing spinors are the solutions to the Killing Equation for a so-called Killing Number.

More formally:

A Killing spinor on a manifold M is a spinor field which satisfies

for all tangent vectors X, where is the spinor covariant derivative, is Clifford multiplication and is a constant, called the Killing number. If then the spinor is called a parallel spinor.

In physics, Killing spinors are used in supergravity and superstring theory, in particular for finding solutions which preserve some supersymmetry. They are a special kind of spinor field related to Killing vector fields and Killing tensors.

External links

"Twistor and Killing spinors in Lorentzian geometry," by Helga Baum (PDF format)

Eric W. Weisstein. "Dirac Operator." From MathWorld--A Wolfram Web Resource.

Eric W. Weisstein. "Killing's Equation." From MathWorld--A Wolfram Web Resource.

"Killing and Twistor Spinors on Lorentzian Manifolds," by Christoph Bohle (postscript format)

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