Feynman diagrams and minimal models for operadic algebras
Abstract
We construct an explicit minimal model for an algebra over the cobarconstruction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate notion of a homotopy equivalence of operadic algebras and show that our minimal model is homotopy equivalent to the original algebra. All this generalizes and gives a conceptual explanation of wellknown results for Ainfinity algebras. Further, we show that these results carry over to the case of algebras over modular operads; the sums over trees get replaced by sums over general Feynman graphs. As a byproduct of our work we prove gaugeindependence of Kontsevich's `dual construction' producing graph cohomology classes from contractible differential graded Frobenius algebras.
 Publication:

arXiv eprints
 Pub Date:
 February 2008
 arXiv:
 arXiv:0802.3507
 Bibcode:
 2008arXiv0802.3507C
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Quantum Algebra;
 18D50;
 57T30;
 81T18;
 16E45
 EPrint:
 18 pages