Why is it hard to extend the Feynman Checkerboard to more than 1+1 dimensions?

The Feynman Checkerboard Wikipedia article states: "There has been no consensus on an optimal extension of the Chessboard model to a fully four-dimensional space-time."

Why is it hard to extend it to more than 1+1 dimensions?

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I saved another paper on the subject, one written at a lower level than some, on my website here: brannenworks.com/plavchan_feynmancheckerboard.pdf It notes that there are issues with the particle in 3 dimensions apparently being superluminal. –  Carl Brannen Jan 28 '11 at 15:37
Thanks for the reference. –  mtrencseni Jan 28 '11 at 15:59
@Carl, if you provide that link as an answer I'll accept it. –  mtrencseni Jan 29 '11 at 7:45
Am I missing something, or is 1+1 not 2? :O –  Noldorin Jan 29 '11 at 18:55
@Noldorin - in this context 3+1 does not equal 2+2. –  Johannes Jan 30 '11 at 0:16
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There's an interesting paper on the subject, written at a lower level than some, on my website here:
http://brannenworks.com/plavchan_feynmancheckerboard.pdf

It notes that there are issues with the particle in 3 dimensions apparently being superluminal with a speed of at least $\sqrt{3}\;c$.

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In 1+1 dimensional spacetime you can split the operator $d^{2}/dt^{2} - d^{2}/dx^{2}$ in a very simple way into a product: $(d/dt - d/dx)(d/dt + d/dx)$. This is not possible in higher dimensions.

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Nice!, I like it. –  Carl Brannen Jan 29 '11 at 22:29
uh? But this is what $\gamma$ matrices are supposed to do for us, in higher dimensions, isn't it? –  arivero Feb 18 '11 at 17:02
Indeed. So if you manage to create an anti-commuting checkerboard, you will be able to generalize the checkerboard model to higher dimensions. –  Johannes Feb 19 '11 at 1:37