Atomic kernels as waves and catastrophes

The presentation of atomic kerrnels as particles requires for the physics duality principle that they get a wave description. This is due to presenting the SU (3) GellMann matrix space by octonians which are obtained by doubling the spacetime quaternions. Their multiplication table is different from the SU (3) matrices. The third presentation of this space is a complex 4-dimensional space where the real spacetime coordinates of a 4-dimensional Euclidean Hilbert space R4 are extended to C4. For getting from Deuteron Cooper pairs NP of a neutron and proton atomic kernels AK, the wave package superpositions for AK need the mass defect of neutrons where kg is changed to inner speeds or interaction energies. For kg octonians have a GF measuring base triple as Gleason operator. Using a projective geometrical norming, C4 is normed to CP³, a projective 3-dimensional space. Its cell C³ has spacetime coordinates C², extended by an Einstein energy plane z3 = (m,f), m mass, f = 1/∆t frequency where mass can be transformed into f by using mc² = hf. If C³ is presented as a real space R6, it can be real projective normed to a real projective space P5 for the field presentation of AK. As field the NP‘s have then a common group speed for AK wave packages superpositions with which AK moves in spacetime C² and also a presentation as a Ψ wave. As probability distribution where they can be energetically found in space serves Ψ* Ψ.