The agenda of next meetings of Krasil'shchik's seminar on geometry of
differential equations at the Independent University of Moscow joint
with the seminar of Laboratories 6 and 82 of the ICS RAS.
On 31 March the seminar meets offline in room 304 of the Independent
University of Moscow, on 19:20 as usual, simultaneously, there will be
broadcast via Zoom.
Speaker: Hovhannes Khudaverdian
Title: Odd symplectic geometry in the BV-formalism
Language: English
Zoom:
https://zoom.us/j/8817121842?pwd=Kytoa1dGaSszaWh1dzY1KzlTUURnQT09Zoom Passcode: 7392
Abstract:
Odd symplectic geometry was considered by physicists as an exotic
counterpart of even symplectic geometry. Batalin and Vilkovisky changed
this point of view by the seminal work considering the quantisation of
general theory in Lagrangian framework, where they considered odd
symplectic superspace of fields and antifields. [In the case of Lie
group of symmetries BV receipt is reduced to the standard Faddeev-Popov
method.]
The main ingredient of the theory, the exponent of the master action, is
defined by the function f such that \Delta f=0, where \Delta is second
order differential operator of the second order:
\Delta=\frac{\partial^2}{\partial x^i \partial\theta_i}, (x^i,\theta_j
are the Darboux coordinates of an odd symplectic superspace.) This
operator has no analogy in the standard symplectic geometry.
I consider in this talk the main properties of the BV-formalism
geometry.
The \Delta-operator is defined in geometrical clear way, and this
operator depends on the volume form.
It is suggested the canonical operator \Delta on half-densities. This
operator is the proper framework for BV geometry. We also study the
groupoid property of BV master-equation; this leads us to the notion of
BV groupoid. We also discuss some constructions of invariants for odd
symplectic structure.
The seminar meets on Wednesday evenings at 19:20 MSK in Zoom,
Meeting ID: 88 17 12 1842
Offline meetings are planned on 31 March, 7 April and possibly 21 April
and 19 May.
--
FROM 210.3.245.*