P^2+Σ2P

Hilbert space is R^3. It seems to be the normal world, although it is very complicated. (X1,X2,X3)*(Y1,Y2,Y3)=X1Y1+X2Y2+X3Y3 X*Y=Y*X ―① (AX1+BX2)*Y=AX1Y+BX2Y X*X≧0, X=0 X and Y are vectors. ∥X∥ is the length which is called norm. X*Y=∥X∥∥Y∥cosθ When X and Y are the same direction, θ is Zero. This is cooling the temperature for the order . Absolute convergence ignore infinity . When you think about noncommutative algebra, the temperature increase. PQ-QP=h/2πi This includes imaginary spaces. PQ-QP is trace. When PQ-QP=0, (h/2πi)^n must be zero. It is impossible, and you need infinite Hilbert spaces. This is chaotic. Therefore, PQ-QP　―① is commutative in R^3, which is cooling the temperature.

This is high temperature and chaotic, which is called Ising model . Jij>0 This is like Big Bang. You can also write this. Expansion is high temperature. Therefore, you can divide it. The division is cooling. Tr is trace. ∴