München 2009 – wissenschaftliches Programm

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 6: Felder und Strings

MP 6.3: Vortrag

Mittwoch, 11. März 2009, 17:00–17:20, M010

Cartesian integration of Grassmann variables over invariant functions — •Mario Kieburg, Heiner Kohler, and Thomas Guhr — Universität Duisburg-Essen, Lotharstraße 1, 47048 Duisburg

Supersymmetry plays an important role in field theory as well as in random matrix theory and mesoscopic physics. Anticommuting variables are the fundamental objects of supersymmetry. The integration over these variables is equivalent to the derivative. Recently [arxiv:0809.2674v1[math-ph] (2008)], we constructed a differential operator which only acts on the ordinary part of the superspace consisting of ordinary and anticommuting variables. This operator is equivalent to the integration over all anticommuting variables of an invariant function. We will present this operator and its applications for functions which are rotation invariant under the supergroups U(k₁/k₂) and UOSp(k₁/k₂).