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 -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).
Posted at January 16, 2008 8:33 PM UTC
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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.
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
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.