I've been looking for a long time and I've not had a lot of luck. I've found sources that use fermions in 3d Euclidean space but I can't find any that explain the Wick rotation from Minkowski space.

This source provides a nice explanation of the Wick rotation procedure for fermions in 4d. However it leaves the odd dimensional case as an open question.

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    $\begingroup$ Related: physics.stackexchange.com/q/21261/2451 $\endgroup$ – Qmechanic Aug 10 '14 at 20:23
  • $\begingroup$ Perhaps one method would be to perform the Wick rotation in 4d and then compactify a spatial direction to a get an (effective) 3d result. One might be able to generalise to higher odd dimensions by compactifying 6d, 8d, etc... in a similar manner. $\endgroup$ – Siraj R Khan Aug 11 '14 at 12:43

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