{\bf Associativity, Octonions and Skyrme Quark-like Models}
The octonions are generally nonassociative, and the associator (ab)c~-~a(bc)~=~[a,~b,~c] leads to uncertainty in the definition of Jacobi identities. However here an identification is found of the associator with a new Chern-Simons...
The S-matrix is a topological approach to quantum field theory. It is the jumping off point for the Veneziano amplitude and the basis for string theory. It is based on the notion of an order for the relationship between different quantum fields, which in a more standard QFT approach is a time...
This is a note on how a Bloch wave analysis of quantum states and fields may be used in quantum field theory and gravitation. This is an approach which uses some results of solid state physics. There have been some approaches of this nature in lattice gauge field theory and there have been...
There are a number of cellular automata quantum models one might consider. The type of model here has some analogues with atoms in a laser trap.
Lawrence B. Crowell
For a black hole which emits a particle the back reaction g~\rightarrow~~g' is a classical convenience. It is almost a Copenhagen-esque treatment of the black hole as a classical system which collapses the decoherent state of the emitted quanta (photons etc). Yet for a small enough black hole...
I am not sure what sBoostrap is, and I suppose that the hexagonal number pattern is related to this. These generations, such as the 60, is half the number of spinor on the M_{12} Mathieu group on the 120-cell or icosahedron. I am not sure if degeneracies are considered here, but 196560 is...
I made a type with 28~=~2^2(2^3~-~1). I had not thought about whether there are integer patterns or sequences associated with the root dimension of groups. It appears as if this pattern pertains to the complexification of these groups G(R)\times G(R)~=~G(C). I might spend a little bit of time...
These numbers are related to Mersenne primes as
6~=~2^1(2^2~-~1)
26~=~2^2(2^3~-~1)
496~=~2^4(2^5~-~1).
It is an interesting pattern. I am not sure whether this amounts to an accident of some sort or whether there is actually something going on here. If there is a connection...
I had thought of some similar ideas. The first is with supersymmetry, where if we think of a SUSY doublet \Phi~=~\phi~+~\xi\psi, for \xi,~\psi as a Grassmann variable and a Dirac field and \phi a boson field, then we can think of there being a,~a^\dagger type operators which interchange the...
Not off topic per se. Lisi's theory might be wrong after all. It has a certain economy to it, and I suspect somehow it is not completely flawed. We do have a question to ponder as to why physics would "choose" one decomposition or irrep according to subgroups and not another.
Lawrence B...
Give me a day or two to respond more fully. I have yet to look into the superconductive E_8 much. As for "different uses" for E_8, that is easy to arrive at. There are multiple ways in which it can be decomposed. A part of my thinking with the modular Leech system with three E_8s is that it...
There has been of late some interest in the idea that constants of physics change, or are variable. João Magueijo has suggested various schemes in which the speed of light could vary. The variability of constants is a bit odd. For instance if \alpha~=~e^2/\hbar c were determined by different...
The three E_8 are a modular system of the \Lambda_{24}. The CL(8) has the 256 elements of the 248 of E_8, or that
E_8~=~Spin(16)~+~128,~120~+~128~=~248~dimensions
is contained in Cl(8)~=~1~+~8~+~28~+~56~+~70~+~56~+~28~+~8~+~1, which is the 240 of the root space of E_8, plus the 8 of...
Mathematically he did this in the "voudou" physics. Smith has a lot of work on some representation theory along these lines, but his work IMO comes up a bit short of the dynamics end of things. I have worked out some aspects of what the breaking of an E_6 might look like with conformal gravity...
I can't find the Quillen paper. I read the start of the Dumitruscu paper. It looks to be fairly canonical differential geometry stuff. I am not sure what the "big idea" is here yet.
Lawrence B. Crowell