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Jan 30, 2012 at 2:21 comment added Ron Maimon @Lagerbaer: Yes, the "i" works in the action, but it changes the sign of the measure in the odd dimension case (because the $d\eta$ s get an "i" factor, so it is equivalent to what I did above.
Jan 29, 2012 at 18:06 comment added Lagerbaer Thanks, that's a good idea. How about I define them as $\psi + i\phi$ and $\psi - i\phi$? Then, the middle terms should still cancel, but I'll get a $+$ sign. Also, for an antisymmetric matrix of odd dimension, the determinant is always 0, no?
Jan 29, 2012 at 17:59 history edited Lagerbaer CC BY-SA 3.0
def of $\xi$ needs a -
Jan 29, 2012 at 14:11 history answered Ron Maimon CC BY-SA 3.0