P^2+Σ2P

G=SU(3)×SU(2)×U(1) G is gauge group . Grand unification theory is expansion of G. We have 4 powers in our nature, which are weak interaction, strong interaction, electromagnetic interaction, and gravity. The integration is so hard because of gravity. G may need super gravity for expansion. There is no space and time. SU(5)⊃SU(3)×SU(2)×U(1) This is corruption of everything, and it must be the beginning. It is very difficult to capture Zero. SO(10)⊃SU(5)×U(1)

Now I got φ. There is no matter in Gauge theory , but scalar potential is for gravity. gσρ(x)→W(x)gσρ(x) Gravity and Electromagnetic Field are integrated. However, there are space and time between x and x0. This is against Gauge theory because of General theory of relativity. Then, Higgs field solved this contradiction. SU(2)×U(1) This is called spontaneous symmetry breaking. Gauge symmetry never be broken, and matter is not Zero.

I use fractal as art , but there are some relations with gauge theory. E is electric field. ∇E=ρ/ε0 ∇B=0 B is Magnetic field. B=∇A A is vector potential. ∇E=-∂B/∂t ∴ ∇(E+∂A/∂t)=0 E+∂A/∂t=-∇φ φ is scalar potential. ∴ B=∇A, E=-∇φ-∂A/∂t This is Gauge symmetry, and the potential is chaotic. φ(x)→φ'(x)=e^iθ*φ(x) e is Electric charge.

This is a mathematical trick. Every square is just the line or Every number is reduced to 1 except for 0 There is chaos, but it is in squares. You can also expand any dimensions, when you accept Zero. Zn=6n 1^2=1 ∴

Sierpinski gasket is fractal, which is the concept of my web site . This is a part of quantum theories, although it is chaotic. Sierpinski gasket is in rule 90 . There are 3 cells, and you pick up the center. There are 2^3=8 patterns, which are just on and off. (0,0,0)→0 (0,0,1)→1 (0.1,0)→0 (0,1,1)→1 (1,0,0)→1 (1,0,1)→0 (1,1,0)→1 (1,1,1)→0 It is called exclusive disjunction . I chose (1,0,0)→1, because a part includes everything in fractal. You can put the part in a spreadsheet infinitely. This isn't Тетрис .

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. ∴