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September 2, 2010
The graphene system is fascinating for quantum field on the sheet are not restricted into being strictly fermionic or bosonic. Under an exchange of particles with state vectors |Ψ_1> and |Ψ_2> there is |Ψ_1Ψ_2> = e^{iθ}|Ψ_2Ψ_1>, which in dimensions > 2 has θ = {0, π} so the exchange is 1 for bosons and -1 for fermions. The spin statistic is defined by π_1(SO(n,1)) which for n > 2 is π_1(SO(n,1)) = Z_2, but for n = 2 is π_1(SO(2,1)) = Z. The first homotopy group indicates that orientation of the spin, which is infinitely cyclic in n = 2. Further this means the standard sequence
1 --> Z_2 --->spin(n) ---> SO(n) ---> 1
does not apply, so spin(2,1) is not a universal covering group. The projective system over SO(2,1) is the braid group B_2, which describes the anyon.
The analogue of a string in graphene is the occurrence of an effective magnetic monopole with the quantum Hall effect. The quantized currents on a graphene sheet with the quantum Hall effect can result in an effective magnetic monopole. The quantum flux of B-field due to currents around the sheet has an effect of setting one of the magnetic poles ---> infinity like the Dirac solonoid monopole. This sets up a duality between the electric and magnetic charges, e and b respectively, so that eb = nħ. This is the T-duality which a Type IIA string has with respect to D2, D4, D6, D8 and D10 branes. In 10 dimensions the T-duality obtains on a D8-brane, and the 11-dimensional duality obtains on a D9-brane, which gives a correspondence between Type IIB and Type IIA strings.
This physics is generalized into Chern-Simons theory. The 2+1 C-S theory is given by a Lagrangian
L = A Λ dA + (2/3)A Λ A Λ A,
Where this Lagrangian defines a cyclicity S = ∫d^3x L, with S --> S + 2πN, for N a winding number. By Poincare duality this is carried over to the 8 dimensional surface as the boundary of the 9 dimensional surface, here the surfaces in fact being D-branes and the two surface a D2-brane bounding a 3-dimensional region. The duality carries this information over to a supersymmetric WZW Lagrangian. The D2-branes exist in a foliation that is in the bulk transverse to C^4/Z^8, for Z^8 a set of discrete points (Z^8 a lattice of charges or roots of the E_8). The transversality condition preserves the anionic structure on the D2 as supersymmetry (N=8 SUSY) on the C^4/Z^8.
Lawrence B. Crowell
post approved
1 --> Z_2 --->spin(n) ---> SO(n) ---> 1
does not apply, so spin(2,1) is not a universal covering group. The projective system over SO(2,1) is the braid group B_2, which describes the anyon.
The analogue of a string in graphene is the occurrence of an effective magnetic monopole with the quantum Hall effect. The quantized currents on a graphene sheet with the quantum Hall effect can result in an effective magnetic monopole. The quantum flux of B-field due to currents around the sheet has an effect of setting one of the magnetic poles ---> infinity like the Dirac solonoid monopole. This sets up a duality between the electric and magnetic charges, e and b respectively, so that eb = nħ. This is the T-duality which a Type IIA string has with respect to D2, D4, D6, D8 and D10 branes. In 10 dimensions the T-duality obtains on a D8-brane, and the 11-dimensional duality obtains on a D9-brane, which gives a correspondence between Type IIB and Type IIA strings.
This physics is generalized into Chern-Simons theory. The 2+1 C-S theory is given by a Lagrangian
L = A Λ dA + (2/3)A Λ A Λ A,
Where this Lagrangian defines a cyclicity S = ∫d^3x L, with S --> S + 2πN, for N a winding number. By Poincare duality this is carried over to the 8 dimensional surface as the boundary of the 9 dimensional surface, here the surfaces in fact being D-branes and the two surface a D2-brane bounding a 3-dimensional region. The duality carries this information over to a supersymmetric WZW Lagrangian. The D2-branes exist in a foliation that is in the bulk transverse to C^4/Z^8, for Z^8 a set of discrete points (Z^8 a lattice of charges or roots of the E_8). The transversality condition preserves the anionic structure on the D2 as supersymmetry (N=8 SUSY) on the C^4/Z^8.
Lawrence B. Crowell
post approved
Hi,
I have many questions about the rotations of a Black Hole .The link of central spheres is important and the mass .
If I take the model of Reissner-Nordström without electric charge and cinetic moment .And the universal link between mas and rotations of spheres ,I suppose the finished universal sphere without rotation because it's the maximum mass and thus the maximum physical energy .
If I take this gravitational singularity ,the codes of quantum spheres ,which are correlated with the number of cosmological spheres ,if all rotates ,that implies a big mass thus a big attraction.
The fact to have this non rotation of the sphere of the Black Hole is logic and is balanced with all universal Black Hole.This attraction permits to decrease the space between stars .The spiral galaxies spherisizes themselves due to this gravity of the Black Hole .
What I find relavant is what the Black Hole turns very slowly.Not 0 moment and electric charge but a very weak rotations around itself(sphereof the black hole)
The main code is in the center in the quantum spheres .
The plan is so important too when we see the design of a galaxy .
The balance about the gravitational curve too is relevant .
The numbers of quantum spheres in rotations around themselves is the key it seems to me .
All is a question of gravity and attraction by increasing of mass thus increasing of activation of quantum spheres .The Dark matter and the center with a contraction can be insert too .The space is quantum sphere without rotation thus without mass but with a code of activation due to the gravity in increasing ,all that permits the spherisation.A Black Hole in this logic decreases its velocity of rotations because the mass increase ,thus the rotations of quantum spheres increase .
It's important to consider all the times what all is balanced and evolves in complexification of increasing of mass ,the cosmological spheres .
In this logic ,normally the velocity of our Earth around itself decreases because its mass increases .Logically .Thus logically too the quantum spheres accelerates or activates othes quantum spheres of the quantum architecture .
Sincerely
Steve
post approved
I have many questions about the rotations of a Black Hole .The link of central spheres is important and the mass .
If I take the model of Reissner-Nordström without electric charge and cinetic moment .And the universal link between mas and rotations of spheres ,I suppose the finished universal sphere without rotation because it's the maximum mass and thus the maximum physical energy .
If I take this gravitational singularity ,the codes of quantum spheres ,which are correlated with the number of cosmological spheres ,if all rotates ,that implies a big mass thus a big attraction.
The fact to have this non rotation of the sphere of the Black Hole is logic and is balanced with all universal Black Hole.This attraction permits to decrease the space between stars .The spiral galaxies spherisizes themselves due to this gravity of the Black Hole .
What I find relavant is what the Black Hole turns very slowly.Not 0 moment and electric charge but a very weak rotations around itself(sphereof the black hole)
The main code is in the center in the quantum spheres .
The plan is so important too when we see the design of a galaxy .
The balance about the gravitational curve too is relevant .
The numbers of quantum spheres in rotations around themselves is the key it seems to me .
All is a question of gravity and attraction by increasing of mass thus increasing of activation of quantum spheres .The Dark matter and the center with a contraction can be insert too .The space is quantum sphere without rotation thus without mass but with a code of activation due to the gravity in increasing ,all that permits the spherisation.A Black Hole in this logic decreases its velocity of rotations because the mass increase ,thus the rotations of quantum spheres increase .
It's important to consider all the times what all is balanced and evolves in complexification of increasing of mass ,the cosmological spheres .
In this logic ,normally the velocity of our Earth around itself decreases because its mass increases .Logically .Thus logically too the quantum spheres accelerates or activates othes quantum spheres of the quantum architecture .
Sincerely
Steve
post approved
For those interested in the subject of black holes, I have started a three part series called, Black Holes Through Outer Space, on the subject. The first paper, Predictable Barriers Precluding Any Consideration of Transversable Black Holes Through Outer Space, is online at scientificblogging,com.
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God bless you physicists--I am unable to comprehend even your most rudimentary explanations.
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