Part I gives the general description of raising vector space W in the power M/L. The result is the new vector space V. In the Part IV we take W - the 8 – dimensional generalization of our 4 – dimensional vector space. Then we raise W in the power 1/3. The result is the 2 – dimensional vector space V. The metric and algebraic tensors for V are the same as in the Part III.
After that we take some vector from V and use it for construction of Lagrangian. And for simplicity we restrict us by only first 4 dimensions of W. Then, from the principle of minimal action, we get the equations for our vector. And we derive that vector from these equations.
Then we define the tensor and vector of energy – momentum for this Lagrangian. And also we find the density of spin tensor and (with the help of the algebraic tensor) the density of spin vector. The numerical cofactor in them is 1/3. So we consider that spin of this vector is 1/3. It coincides with the power of W for V (vector space we took our vector from).
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