From Special Relativity to embedded generators in Cartan subalgebras of rank-4 spin algebras

Zen-chen Leon

paper

From Special Relativity to embedded generators in Cartan subalgebras of rank-4 spin algebras

arXiv:1610.09913

Abstract

Starting by revisiting Special Relativity, here we provide a reliable characterization of the entire 4-dimensional fundamental structures in our reality where the frame of discrete tangent space of $F^{1, 3}$ is quantized to massless, zero-momentum particles distributing on a 4-dimensional regular base ${N \cdot c_{α}}$ with metric $B (c_{α}, c_{β}) = δ_{α β} = diag (+, +, +, +)$ , determining the constant $c$ locally, as well as instant characterizations on all particles moving along the proper time of $τ \in N$ . Together with $ϕ_{IV}$ on 1-dimensional space ${N \cdot c_{4}}$ of $B (c_{α}, c_{4}) = 0$ , the quantized particles of tangent frame are split anti-symmetrically from roots $γ_{α 4}$ in a rank-4 Lie algebra with exactly $c_{α}$ the generators of its Cartan subalgebra. As with the combined frame-Higgs valued in $γ_{α 4}$ , every massive particle is related to some split frame and Higgs to obtain its unique quantized relative 3-velocity, 4-velocity, and rest mass under the restriction of Pauli Exclusion Principle at each $τ$ . We calculated the domains $S_{i} \subset F$ and $S_{0} \subset F_{\geq}$ in $F_{\geq} \oplus F^{3}$ the spacetime in which a massive particle $p$ evolves with ${x^{α}}$ of $x^{α} \in S_{α}$ the coordinate its Center-of-Mass under an eligible observation that $∣ F ∣ = ∣ F_{\geq} ∣ = ℵ_{0} < ∣ R ∣$ , available for post-Newtonian approaches.

arXiv comment17 pages, 0 figures

From Special Relativity to embedded generators in Cartan subalgebras of rank-4 spin algebras

Abstract

References in corpus (41)