A Cubic Pure Half-Spinor Approach to High Performance Photon-Counting Computerized X-ray Tomography – Transcendence of the Brauer Mirror Symmetry Functor –

Abstract

The goal of this paper is to present a spectral theory of advanced photon-counting computerized X-ray tomography, which is a promising microelectronical semiconductor wafer X-ray technique on the verge of becoming clinically feasible and has the potential to dramatically alter the clinical application of computer-aided medical diagnosis in the upcoming decades. In analogy to the deep fact that any real division algebra has dimension 1, 2, 4 or 8, the isogeneous third Galois cohomological, mirror symmetrical approach to high spatial resolution spectral photon-counting computerized tomography establishes that the exceptional Lie group $$\textrm{Spin}(8,\mathbb {R})$$ Spin ( 8 , R ) is the only one of the spin group spectrum $$\{\textrm{Spin}(n,\mathbb {R})\mid n \ge 1\}$$ { Spin ( n , R ) ∣ n ≥ 1 } to admit a triality automorphism. It is the exceptional phenomenon of triality which is able to produce by the spin representation theory of the exceptional Lie group of octonions $$\mathbb {O}$$ O the spectral shaped digital signals of spectral photon-counting computerized X-ray tomography. Similarly to spin echo magnetic resonance tomography, the mathematical approach to spectral high performance computerized tomography is based on the isogeneously invariant, projectively weighted, symplectic coadjoint orbit picture $$\mathfrak {Lie}(\mathcal {N})^*/\textrm{CoAd}(\mathcal {N})$$ Lie ( N ) ∗ / CoAd ( N ) of the real 3-dimensional Heisenberg unipotent Lie group $$\mathcal {N}$$ N of type $$\textrm{GL}(3,\mathbb {R})$$ GL ( 3 , R ) , and its solvable diamond toric Lie group extension.