Multiple Variables
Integration over multiple variables is defined by Fubini's theorem:
Note that the sign of the result depends on the order of integration.
Suppose now we want to do a substitution:
where as usual (ξj) implies dependence on all ξj. Moreover the function θi has to be an odd function, i.e. contains an odd number of ξj in each summand. The Jacobian is the usual matrix
the substitution formula now reads as
Read more about this topic: Grassmann Integral
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