... by the 1-component Dirac 2.0 quanta energy system with positive masses, while the classical ((H(1)-domain based !) waves still travel with the speed of light.


Note: The group SU(2) is important in describing the transformation properties of spinors. It is isomorhic to the unit quaternions S(3). In SMEP the group SU(2) describes the weak force interaction with 3 bosons W(+), W(-), Z.

Note (the quaternion rotation operator): The quaternions provide an appropriate field to address the „translation-rotation“ (linear and angular rotation) „permutation“ requirement. The perhaps primary application of quaternions is the quaternion rotation operator. This is a special quaternion triple-product (unit quaternions and rotating imaginary vector) competing with the conventional (Euler) matrix rotation operator. The quaternion rotation operator can be interpreted as a frame or a point-set rotation, (KuJ). Its outstanding advantages compared to the Euler geometry are

- the axes of rotation and angles of rotation are independent from the underlying coordinate system and direct readable

- there is no need to to take care about the sequencing of the rotary axes.

Note: According to the deductive structure of the dynamic quanta scheme the H(1/2) energy field based dynamic fluid particle (solving the 3D-NSE problem) may be interpreted as a dynamic approximation quantum element type (quanta) of the three Dirac 2.0 quantum types. The prize to be paid for this are hydrodynamic instabilities accompanied by turbulences, (MiD). 

Note: Schrödinger's "two ways of producing orderlines" (i.e., by which orderly events can be produced) are (1) the "statistical mechanism", which produces "order from disorder", and (2) the new one, which produces "order-from-order", (ScE1) p. 80. Accordingly, the approximation process, where "Dirac 2.0 based dynamic quanta aproximated by H(1/2)-based dynamic quanta", is about a "disorder-from-order" mechanism. Then the next aggregation approximation layer, where "H(1/2)-based dynamic quanta are approximated by H(1)-based mechanical quanta", becomes again the well-known thermo-statistical "order-from-disorder" mechanism.

Note: For the mathematical approximation theory in Hilbert scales and related extensions and generalizations regarding the fundamental "exponential decay" Hilbert space we refer to (NiJ), (NiJ1).