Decorated trees for Koszul-Tate resolutions and ghosts

Speaker: Thomas Strobl

Abstract: Koszul-Tate resolutions are the key ingredient in the Batalin-Vilkovisky (BV) and the Batalin-Fradkin-Vilkovisky (BFV) formalisms. Such resolutions have been known explicitly only in a very limited number of cases. And while the Tate algorithm shows existence, it almost always leads to an infinite amount of computations to be performed.

We provide an alternative approach where the generators of the Koszul-Tate resolutions become trees, decorated by the generators of an initially given and much easier to find module resolution. If the module resolution is finite (like for ideals in a polynomial algebra), only a finite number of computations are needed to arrive at our arborescent Koszul-Tate resolutions.

We show how to apply this for BFV or BV in the finite dimensional setting. The former provides an algebraic description of singular coisotropic reduction, which we will make explicitly for the case of rotations acting on the cotangent bundle of R^3.

Time: 15:00, Tuesday, Sept. 24, 2024

Location: Room 1410, Block A, No. 657 Songhu Road, Yangpu District, Shanghai