Here it is shown that the known forces of nature unfold in parallel with an exact decomposition of the geometric algebra Cl3,1 of spacetime. Up to an important common scalar this decomposition is a partition into a positive definite commutative graded space of strong forces and two negative non-commutative spaces with a quaternion structure for weak and other fields. The 6 fundamental spaces of strong forces are acted on by a rank 2 Lie algebra L = sl Cl (2, R) × so Cl (3, R) of dimension 8 which brings in an isotropy group of the neutrinos, the flavour and colour symmetries and an isotropy of the weaker forces. The standard model, in an improved form, is a feature of the Clifford algebra of spacetime, and relativity as Lorentz invariance reduced to dimension (2, 1) is compatible with quantum theory. The whole Lorentz group cannot be, however, a property of physical motion. Due to the total exploitation of the whole geometric space and its convincing logical structure, the author believes there is at present no better algebraic model for the totality of known symmetries of physical dynamics. Prologue:This is to give you a brief solution to an old riddle, namely how relativity can be united with quantum physics and where the standard model stems from. In the paper it is shown that the algebra of matter has three components which have what I call a definite signature. The first component Ch is positive and is a sum of six positive definite commutative spaces. In my previous writings Advances in Applied Clifford Algebras 15 No. 2, 271-290 (2005)
The tree which results from the application of the Sonquist and Morgan method is based on the principle of dichotomizing the population at each point according to one of the independent variables in such a way as to explain as much variance of the dependent variables as possible. Confronted before applying this tree-analysismethod, with a distribution of the dependent variable, we may imagine that this distribution was the result of some process Pj.
Purpose of a minimal theory is to achief most with least. Least may be for example the spacetime algebra. But the symmetric unitary group SU(3) is nota part of any real Clifford algebra of 4-dimensional space, especially not of the algebra C11,3 of the Minkowski spacetime, nor of the algebra Cl3,~ in the opposite metric. Therefore we can ask how quantumchromodynamics enters into the theory. A ¡ answer is that the group SU (3) is an object of both the complexified algebras C | Cll,3 and C|To show this we first define six color spaces which ate spanned by conjugate triples of commuting base elements. These contain the six idempotent lattices that can be located in Cl3,l. Their images exist in both (J | Cll,3 and C | Cl3,1. Further in each color space there is defined ah octahedral orientation stabilizer group which fixates one lepton and color rotates the states in its quark family. Thus quantum numbers of strong interacting fields such as isospin, charge, hypercharge and color turn out as geometric properties. Next we ask if the axtificialty of complexification can be avoided. The answer is yes. Defining the class of Clifford algebras with proper imaginary unit it turns out that Cll,s and Cls.~ do not belong to this class. But C14,1 and C11,6 do. It is shown that in the latter algebra the whole color space Ansatz can be established and the generators of SU(3) represented most naturally and without complexification. That the proposed theory becomes a physically true statement requires that there exists a non rank preserving freedom of motion within the constituents of primitive idempotents, that is, transpositions among conjugate triples in color space.
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