Floer Homology Language TANAKA Akio Note 7 Quantization of LanguageTheorem1(Barannikov, Kontsevich 1998)<.,.>, ° defines structure of Frobenius manifold at neighborhood of H's origin.2(Kontsevich 2003)There exists φk : EkΠ2(Γ(M;Ω(M))) → Π2CD(A, A), k = 2, ... . is L∞ map.Explanation1(Local coordinates of Poisson structure){f, g} 2(Map){.,.} : C∞ × C∞ →C∞The map has next conditions.(i) {.,.} is R bilinear,{f, g} = - {g, f}.(ii) Jacobi law is satisfied.(iii) {f, gh} = g{f, h} + h{f, g}3(Gerstenharber bracket)45678( )Manifold M= R2nCoordinates p, qDifferential form w = dqidpiSubset of C∞( R2n ) AElement of A F Differential operator of R2n D(F)D({F, G}) ≡ [D({F}, D({G}][Image 1]Quantization of language is defined by theorem (Kontsevich 2003).[Image 2]Complex unit is seemed to be essential for mirror symmetry of language by explanation 8.[References] Quantum Theory for language / Synopsis / Tokyo January 15, 2004Mirror Theory / Tokyo June 5, 2004For WITTGENSTEIN Ludwig / Position of Language / Tokyo December 10, 2005Tokyo June 24, 2009 Sekinan Research Field of Language