Integration of Grassmann variables over invariant functions on flat superspaces

Details Integration of Grassmann variables over invariant functions on flat superspaces Integration of Grassmann variables over invariant functions on flat superspaces

2008-09-16

arxiv.org/abs/0809.2674v2

J.Math.Phys.50:013528,2009

Physics

Mathematical Physics

31 pages

Scientific paper

10.1063/1.3049630

We study integration over functions on superspaces. These functions are invariant under a transformation which maps the whole superspace onto the part of the superspace which only comprises purely commuting variables. We get a compact expression for the differential operator with respect to the commuting variables which results from Berezin integration over all Grassmann variables. Also, we derive Cauchy--like integral theorems for invariant functions on supervectors and symmetric supermatrices. This extends theorems partly derived by other authors. As an physical application, we calculate the generating function of the one--point correlation function in random matrix theory. Furthermore, we give another derivation of supermatrix Bessel--functions for U(k_1/k_2).

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