Slides: On the BV-Formalism (BV Part XI)
Posted by Urs Schreiber
In the process of wrapping up what has happened so far (part I, II, III, IV, V, VI, VII, VIII, IX, X) I am working on this set of pdf-slides (should be printable, no fancy overlay tricks this time; if you read it online, navigate like a web-site (use your pdf-reader’s back-button!))
Posted at January 16, 2008 8:33 PM UTCAbstract. We try to understand the Batalin-Vilkovisky complex for handling perturbative quantum field theory. I emphasize a Lie -algebraic perspective based on [Roberts-S., Sati-S.-Stasheff] over the popular supergeometry perspective and try to show how that is useful. A couple of examples are spelled out in detail: the -brane, ordinary gauge theory, higher gauge theory. Using these we demonstrate that the BV-formalism arises naturally from a construction of configuration space from an internal hom-object following in spirit, but not in detail, the very insightful [AKSZ, Roytenberg] (discussed previously).
Re: Slides: On the BV-Formalism (BV Part XI)
An incorporation of the notion of BRST-BV complexes from something like inner homs on differential graded commutative algebras into the general framework of -connections is now appearing in section 9.3 of -connections and applications to String- and Chern-Simons -transport.
The underlying Yoga with smooth spaces and their algebras of differential forms appears in section 5.1.
The link connecting all this is the concept of the charged -particle, appearing now as definition 38 on p. 78, featuring here internal to DGCAs.
There would be more to say about the BV quantization of the -particle/-brane charged under a Lie -algebra valued connection, but it’s a start.