sekinanlogoshome
Floer Homology Language
TANAKA Akio
Note7
Quantization of Language
Theorem
1
(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.
Explanation
1
(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)
4
5
6
7
8
( )
Manifold M= R2n
Coordinates p, q
Differential form w = dqidpi
Subset of C∞( R2n ) A
Element 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, 2004
Mirror Theory / Tokyo June 5, 2004
For WITTGENSTEIN Ludwig / Position of Language / Tokyo December 10, 2005
Tokyo
June 24, 2009
Sekinan Research Field of Language
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