Floer Homology Language
Note2
Supersymmetric Harmonic Oscillator
1
Riemannian manifold X
Vector field over X v
All the zero points of v Compact subset of X
Tangent vector bundle of X TX
Clifford module added Z/Z2 degree WX
2
Definition of WX
Here exterior product from left is expressed by
. 
.
Cotangent vector bundle of X T*X
X has Riemannian metric.
TX
T*X
3
Vector field v
Exterior differentiation d
Formally conjugate operator d*
TX T*X
Differential form corresponded with v
Triplex (WX, DX, hX,v) is defined by the next.
4
X is Euclid space E.
Vector field over E v : E →T*E
TE = E × E
hE = hE,v
Triplex (WE, DE, hE) is called supersymmetric harmonic oscillator.
5
Distance of vector field |q|
= d(|q|2/2)
Supersymmetric harmonic oscillator over E is expressed by DE,t = DE + thE.
DE,t = Q + Q*
Q =
Q* =
6
Supersymmetric harmonic oscillator is seemed as <meaning minimum>.
On <meaning minimum>, refer to the next.
1
Riemannian manifold X
Vector field over X v
All the zero points of v Compact subset of X
Tangent vector bundle of X TX
Clifford module added Z/Z2 degree WX
2
Definition of WX
Here exterior product from left is expressed by
. .Cotangent vector bundle of X T*X
X has Riemannian metric.
TX
T*X3
Vector field v
Exterior differentiation d
Formally conjugate operator d*
TX
T*XDifferential form corresponded with v
Triplex (WX, DX, hX,v) is defined by the next.
4
X is Euclid space E.
Vector field over E v : E →T*E
TE = E × EhE = hE,v
Triplex (WE, DE, hE) is called supersymmetric harmonic oscillator.
5
Distance of vector field |q|
= d(|q|2/2)Supersymmetric harmonic oscillator over E is expressed by DE,t = DE + thE.
DE,t = Q + Q*
Q =
Q* =
6
Supersymmetric harmonic oscillator is seemed as <meaning minimum>.
On <meaning minimum>, refer to the next.
From Cell to Manifold / Cell Theory / Tokyo June 2, 2007
Word and Meaning Minimum / Energy Distance Theory / Tokyo September 22, 2008
Amplitude of Meaning Minimum / Complex Manifold Deformation Theory / Tokyo December 17, 2008
Generating Function / Symplectic Language Theory / Tokyo March 17, 2009
Word and Meaning Minimum / Energy Distance Theory / Tokyo September 22, 2008
Amplitude of Meaning Minimum / Complex Manifold Deformation Theory / Tokyo December 17, 2008
Generating Function / Symplectic Language Theory / Tokyo March 17, 2009
7
Distance of supersymmetric harmonic oscillator is seemed as <distance> of <meaning minimum>.
On <distance>, refer to the next.
Distance of supersymmetric harmonic oscillator is seemed as <distance> of <meaning minimum>.
On <distance>, refer to the next.
I first clearly declared <distance> on language in this theory.
[References]
Below papers are partially developed on <distance> from
[References]
Below papers are partially developed on <distance> from
.
Actual Language and Imaginary Language / Tokyo September 23, 2004
Distance / Distance Theory Algebraically Supplemented / Tokyo Ocotber 26, 2007
Finsler Manifold and Distance / Energy Distance Theory / Tokyo November 7, 2008
Distance of Word / Complex Manifold Deformation Theory / Tokyo November 30, 2008
Distance / Distance Theory Algebraically Supplemented / Tokyo Ocotber 26, 2007
Finsler Manifold and Distance / Energy Distance Theory / Tokyo November 7, 2008
Distance of Word / Complex Manifold Deformation Theory / Tokyo November 30, 2008
To be continued
Tokyo May 6, 2009
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