Seminar Quantenphysik und Geometrie
Batalin-Vilkovisky Formalism

Bahns, Cortes, Fredenhagen, Louis, Richter und Schweigert

The Batalin-Vilkovisky formalism provides the modern approach to field theories with gauge symmetries. It is indispensable for supergravity theories. Mathematically, it provides an interesting combination of the Koszul complex with the Chevalley Eilenberg complex. Our goal is to understand these relations, see e.g. [St].

1. Talk: BRST and BV Quantization (Vid Stojevic, Geomatikum, 25.10.2007)
An overview over the BV formalism in the language of classical field theory.
Literature: the talk can be based on [FHM], supplementary material [He1] and [He2]

2. Talk: BV formalism: a mathematical (p)review (Christoph Schweigert, DESY, 8.11.2007 and Geomatikum 22.11.2007)
An overview over mathematical aspects of the BV formalism
Literature: [Li,St]

3. Talk: Cohomology of Lie algebras (Fridolin Roth, Geomatikum, 20.12.2007)
Show how the cohomology of Lie algebras arises in the study of invariants.
There can be a crash course on Tor and Ext, or one can simply reduce it to the Chevalley-Eilenberg resolution.
Examples. Possibly mention the relation to de Rham cohomology of the assocaited Lie group.
Literature: the talk can be based on Chapter 10 of [Lo]

4. Talk: Koszul complex (Urs Schreiber, DESY, 17.01.2008)
The Koszul complex, its definition, description of quotients
Examples
Literature: Chapter 17 in [Eis]

4. Talk: Homological perturbation theory (Birgit Richter, DESY, 17.4.2008)
Handout and full version of the talk.

Literature