geoff paper

Geoff's Paper PhL 6.11.08 He seems to be playing with group theory in an attempt to support S-matrix theory, somehow. The paper spends most of it's time reviewing another paper known as Reference 2. My first reaction is that the paper is a hoax that seems real only because the author makes no spelling or grammatical errors. The term preon refers to sub-quark objects or alternatives to quarks that are supposed to provide a simple theory of particles. Wiki suggests that preons are not very well accepted by the physics "community", no surprise there. A Fock space is the particle Hilbert space we always use. A Fock space vector might be |n1,n2, ....> where the ni are the numbers of each non-interacting particles . Think of a direct product of single particle states. The Lorentz Group (without reflections) has irreducible representations usually indicated as (m,n). Parity takes this and turns it into (n,m). The Dirac electron is (1/2,0) x (0,1/2) for this reason. The generators of the Lorentz group Lie algebra are the 6 distinct objects M and we can find in these the three rotation generators Ji and the three boost generators Ki. In general, the Casimirs here are associated with "spin". The Poincare group takes the 6 generators just mentioned, the M of the Lorentz group, and adds to them the four generators P of translations in space and time to get the 10 parameter Poincare group. Here is the familiar Lie algebra of the Poincare group: One Casimir of the Poincare group is PP = m2, mass (squared). Wigner is associated with this group theory stuff. The phrase "discrete quantum cosmology" seems to be a Geoff term only. The names Gelfand and Naimark are associated with a fancy theorem in the world of algebra involving rings and such, with emphasis on "C* algebras". I suspect that Reference 2 is an earlier paper that Geoff wrote and which I found on line, has a few more equations. The term "left Lorentz group" relates to combining groups to somehow represent physics. Here is some text from a paper Here we need left and right groups because we need two "chiralities". Typical gobbledygook. Milne died in 1950. " From 1932 he also worked on the problem of the "expanding universe" and in Relativity, Gravitation, and World-Structure (1935), proposed an alternative to Albert Einstein's general relativity theory. His later work, concerned with the interior structure of stars, aroused controversy. Milne was president of the Royal Astronomical Society, 1943–1945." So doubtless an interesting fellow. He wrote a book in 1935 called in which he built a model for the universe consistent with special relativity.