Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-06-10
J.Phys.A41:315402,2008
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, LaTeX, 4 eps figures
Scientific paper
10.1088/1751-8113/41/31/315402
We generalize the computation of Feynman integrals of log divergent graphs in terms of the Kirchhoff polynomial to the case of graphs with both fermionic and bosonic edges, to which we assign a set of ordinary and Grassmann variables. This procedure gives a computation of the Feynman integrals in terms of a period on a supermanifold, for graphs admitting a basis of the first homology satisfying a condition generalizing the log divergence in this context. The analog in this setting of the graph hypersurfaces is a graph supermanifold given by the divisor of zeros and poles of the Berezinian of a matrix associated to the graph, inside a superprojective space. We introduce a Grothendieck group for supermanifolds and we identify the subgroup generated by the graph supermanifolds. This can be seen as a general procedure to construct interesting classes of supermanifolds with associated periods.
Marcolli Matilde
Rej Abhijnan
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