### 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 UTC

Abstract.We try tounderstand the Batalin-Vilkovisky complexfor handling perturbative quantum field theory. I emphasize aLie $\infty$-algebraic perspectivebased on [Roberts-S., Sati-S.-Stasheff] over the popular supergeometry perspective and try to show how that is useful. A couple ofexamplesare spelled out in detail: the $(-1)$-brane, ordinary gauge theory, higher gauge theory. Using these we demonstrate that the BV-formalism arises naturally from a construction ofconfiguration space from an internal hom-objectfollowing 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 $L_\infty$-connections is now appearing in section 9.3 of $L_\infty$-connections and applications to String- and Chern-Simons $n$-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 $n$-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 $n$-particle/$(n-1)$-brane charged under a Lie $n$-algebra valued connection, but it’s a start.