Celebratio Mathematica — Schwarz

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Works connected to Andrei Yu. Mikhailov

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A. Mikhailov, A. Schwarz, and R. Xu: “Cohomology ring of the BRST operator associated to the sum of two pure spinors,” Modern Phys. Lett. A 28 : 23 (2013), pp. article no. 1350107, 6 pages. MR 3085958 Zbl 1279.81052 ArXiv 1305.0071 article

Renjun Xu	Related
Andrei Yu. Mikhailov	Related

A. Mikhailov and A. Schwarz: “Families of gauge conditions in BV formalism,” J. High Energy Phys. 2017 : 7 (2017), pp. article no. 063, 25 pages. MR 3686735 Zbl 1380.81371 ArXiv 1610.02996 article

In BV formalism we can consider a Lagrangian submanifold as a gauge condition. Starting with the BV action functional we construct a closed form on the space of Lagrangian submanifolds. If the action functional is invariant with respect to some group \( H \) and \( \Lambda \) is an \( H \)-invariant family of Lagrangian submanifold then under certain conditions we construct a form on \( \Lambda \) that descends to a closed form on \( \Lambda/H \). Integrating the latter form over a cycle in \( \Lambda/H \) we obtain numbers that can have interesting physical meaning. We show that one can get string amplitudes this way. Applying this construction to topological quantum field theories one obtains topological invariants.