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I am quite familiar with use of Wick rotations in QFT, but one thing annoys me: let's say we perform it for treating more conveniently (ie. making converge) a functional integral containing spinors; when we perform this Wick rotation, in a way we change the metric to (-,+,+,+) to (+,+,+,+), so the invariant group is no more SO(3,1) but SO(4) and (SO(4) being compact and the spinor representation non unitary) spinors don't carry finite dimensional representation of this group. So I feel like we shouldn't be talking anymore about this objects, but only about vectors of SO(4).

Is my fear justified? or where am I wrong in my reasoning?

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You may find this paper interesting: arxiv.org/abs/hep-th/9611043 –  Qmechanic Feb 21 '12 at 16:48
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Could you specify more precisely where is the problem? Probably, illustrate it with some functional integral. –  Misha Feb 21 '12 at 17:06

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