Abstract: |
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 \Delta S + 1/2 {S,S} = 0. The CME is defined in a differential graded (dg) Lie algebra, whereas the QME is defined in a space V[[h]] of formal power series or V((h)) of formal Laurent series with values in a dg-BV-algebra V or a bi-dg-Lie algebra. A generalization of classical deformation theory based on the QME may be thought of as quantized deformation theory. Examples include cohomological field theory and string-field theory. Quantum deformation functor and its representability will also be discussed in the talk. |