Nucleosynthesis in Thin Layers (eBook)

2.5.Antimatter as a mean bifurcation rate

The Dirac Sea, i.e., a system of positive and negative energies and masses is viewed as an irreducible inflection tangent (bifurcation line) algorithm of four points 1,2,1’,2’ on a Kummer surface connected with a vertex part Γ(1,2,;1’,2’) as inflection tangent 2,1’ of an elliptic curve with points 1,2’. The vertex part Γ(1,2;1’,2’) denotes a symmetrized curve- tangent relation on a Kummer surface of a floating object. A 2x2 matrix dF(X,Y) for inflection tangents [19] is cast into a 4x4 form.Two rational world points X are connected by a SE(3) step with SE(3) screw s(A, a) for SE(3) matrix S(A, a) with a nilpotent matrix N0= S(S2-A2)/A2=0. Then dF(X,Y) and S(A, a) satisfy Dirac-like equations where the bi spinor ψs is an invariant expansion of the K(X) differential √d2 as square root of for simplest cycles of the map. A second definition of ψs arises from the exact expression of F(X,Y) which similar to the expression for the cross-ratio λ. Then ψs ere eigenstates of a matrix λ=λm/m ± ½ which defines the relation between mass and f(√Δ). The trivial fourth-order SE(3) term S4(A, a)-A2S2 =0 generalizes the mass generating Higgs Ginzburg-Landau term of phase transitions. The Mandelbrot map can be mapped to a Tschirnhaus- Hermite substitution of a lemniscate. The 4x4 nilpotent matrix N0= S(A2-S2)/A2=0 is equivalent to a Dirac equation E2-m2-p2=0 with λ=λ(m) and to where coordinate and spin index μ and s ranges from 1 to 4. Two periodicities appear: Sharkovskii’s ordering, and a Monster group and Minkowski bound structure of the elliptic invariant j(ω) localized in two regions. Bifurcation is equivalent to motion of dark matter of four points which can be visualized as tidal forces. For simplest cycles f(ω) fluctuations localize ψ-fluctuations as spatial SE(3) steps on K(X). A stationary bifurcation rate of simplest cycles creates masses +m and -m in