Talk:Killing spinor

I'm prepared to say that this is too vague to be useful. Charles Matthews 04:18, 2 Aug 2004 (UTC)

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What about something like:

A Killing spinor on a manifold M is a spinor field $\varphi$ which satisfies

${\mathrm{\nabla }}_X\varphi =\lambda X.\varphi$

for all tangent vectors X, where $\mathrm{\nabla }$ is the spinorally covariant derivative and $\lambda$ is a constant, called the Killing number. If $\lambda =0$ then the spinor is called a parallel spinor.

Uses:

• Physics - supergravity and string theory (in particular used for finding solutions which preserve some supersymmetry)
• Mathematics - ?

Dmr2 14:28, 26 Aug 2004 (UTC)

What $\lambda X.\varphi$ means?

Tosha 16:17, 26 Aug 2004 (UTC)

The dot in $X.\varphi$ means Clifford multiplication. Just removed

The Killing equation is analogous to Maxwell's equations, but abstracted to higher dimensions.

from the main page. I don't think the Killing equation has anything to do with Maxwell's equations. Dmr2 09:59, 27 Aug 2004 (UTC)

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