Contents

Idea

See at relation between BV and BD.

Definition

The underlying graded vector spaces are

$BD \coloneqq P_0 \otimes \mathbb{R}[ [\hbar] ]$

and the differential is

$d ( (-)\cdots (-)) = \hbar \{-,-\} \,.$

(…)

algebraic deformation quantization

dimensionclassical field theoryLagrangian BV quantum field theoryfactorization algebra of observables
general $n$P-n algebraBD-n algebra?E-n algebra
$n = 0$Poisson 0-algebraBD-0 algebra? = BD algebraE-0 algebra? = pointed space
$n = 1$P-1 algebra = Poisson algebraBD-1 algebra?E-1 algebra? = A-∞ algebra

References

The BD operad was introduced in

A review in the context of factorization algebras of observables is in section 2.4 of

• Kevin Costello, Owen Gwilliam, Factorization algebras in perturbative quantum field theory : $P_0$-operad (wikilass=‘newWikiWord’>P_0%20operad?</span>), pdf)

Last revised on December 21, 2016 at 16:15:49. See the history of this page for a list of all contributions to it.