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I'm an ex-twistor theorist who worked on the original twistor programme until 1984, when I decided that I wasn't clever enough to be a mathematical physicist ! Have worked in industry since then and am now trying to catch up on what has been happening in physics.


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comment How algebraic geometry and motives appears in physics?
Related: physics.stackexchange.com/q/29424
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comment single-particle wavepackets in QFT and position measurement
Also relevant to the discussion of wavefunctions in QFT is the question of the causal behaviour of the "naive" wavefunction (not the Schroedinger wavefunctional that Trimok is referring to). This is discussed here
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comment Euclidean black hole extrinsic curvature
Not sure how to answer your question fully, but since the horizon is two dimensional, there are two normals with respect to which extrinsic curvatures can be defined. If $n$ is one of the normals, the ext. curvature for that direction is $\mathcal{L}_ng_{\mu\nu}$ and so vanishes if $n$ is a Killing vector for your metric. In your Euclidean case this Killing property is what you'd need to show presumably.