On the quantized representations ofU(1)×SU(2) as time-space model

Summary

On the Lie groupU(1)×SU(2) and its tangent Lie algebraR ⁴ as parameter manifold for global and local time-space, the characteristic structures −e.g. fundamental unitary and «noncompact pseudounitary» representations, Maurer-Cartan forms (vierbein), Lorentz metric etc.—are considered in the associated quantum algebra of Fermi type. The complexified basicU(1)×SU(2) orbits, arising as Weyl spinor-isospinor fields on time-space, have a Lorentz-invariant dynamics. A harmonic analysis on the tangent spaceR ⁴ with the induced Poincaré group action uses both unitary and «noncompact pseudounitary» representations for the time translationsR and the Euclidean position space groupSO(3)× _s R ³ respectively compensating each other on the time and position space connecting light-cone. In a first approximation, unitary and «noncompact pseudounitary» representations can be related to each other in flat time-space by a characteristic mass ratio of the orderM ₀/m ₀≃exp[(2π)²]≃10¹⁷ which may be compared with the ratio between Planck and weak boson mass.