## January 16, 2008

### 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!))

Abstract. We try to understand the Batalin-Vilkovisky complex for handling perturbative quantum field theory. I emphasize a Lie $\infty$-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 $\left(-1\right)$-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).

Posted at January 16, 2008 8:33 PM UTC

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## 1 Comment & 2 Trackbacks

### 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/$\left(n-1\right)$-brane charged under a Lie $n$-algebra valued connection, but it’s a start.

Posted by: Urs Schreiber on January 22, 2008 11:07 AM | Permalink | Reply to this
Read the post Smooth 2-Functors and Differential Forms
Weblog: The n-Category Café
Excerpt: An article on the relation between smooth 2-functors with values in strict 2-groups, and an outline of the big picture that this sits in.
Tracked: February 6, 2008 1:07 PM
Read the post Frobenius algebras and the BV formalism
Weblog: The n-Category Café
Excerpt: Bruce Bartlett is looking at the latest article by Cattaneo and Mnev on BV-quantization of Chern-Simons theory.
Tracked: November 14, 2008 1:32 PM

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