BD operad

The *Beilinson-Drinfeld operad* is the operad whose algebras over an operad are BD algebras.

See at *relation between BV and BD*.

The underlying graded vector spaces are

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

and the differential is

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

(…)

**algebraic deformation quantization**

dimension | classical field theory | Lagrangian BV quantum field theory | factorization algebra of observables |
---|---|---|---|

general $n$ | P-n algebra | BD-n algebra? | E-n algebra |

$n = 0$ | Poisson 0-algebra | BD-0 algebra? = BD algebra | E-0 algebra? = pointed space |

$n = 1$ | P-1 algebra = Poisson algebra | BD-1 algebra? | E-1 algebra? = A-∞ algebra |

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.