Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

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!))

On the BV-Formalism

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 (1)(-1)-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

TrackBack URL for this Entry:

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 L_\infty-connections is now appearing in section 9.3 of L L_\infty-connections and applications to String- and Chern-Simons nn-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 nn-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 nn-particle/(n1)(n-1)-brane charged under a Lie nn-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

Post a New Comment