Quantum master equation and deformation theory

Classical deformation theory is based on the Classical Master Equation (CME), a.k.a. the Maurer-Cartan
Equation: dS + 1/2 [S,S] = 0. Physicists have been using a quantized CME, called the Quantum Master Equation
(QME), a.k.a. the Batalin-Vilkovisky (BV) Master Equation: dS + h \DeltaS + 1/2 {S,S} = 0. The CME is defined in a dg
Lie algebra g, whereas the QME is defined in a space V [[h]] of formal power series with values in a differential graded
(dg) BV algebra V. One can anticipate a generalization of classical deformation theory arising from the QME or quantum
deformation theory.


There are a few papers which may be viewed as making first steps in abstract quantum deformation theory: Quantum
Backgrounds and QFT by Jae-Suk Park, Terilla, and Tradler; Modular Operads and Batalin-Vilkovisky Geometry by
Barannikov; Smoothness Theorem for Differential BV Algebras by Terilla; and Quantizing Deformation Theory by Terilla.

Further steps in quantum deformation theory will be discussed in the talk.