| I. Quantum Fields as Carriers of the Structure of Space-Time in the Special Grand Unification Model (G. Stavraki) |
| | 1. Introduction |
| | 2. Model |
| | | A. Motivation and the general description of the basic equations of the model |
| | | B. Heuristic derivation of equation (2) in the framework of the correspondence principle |
| | | C. Reduction of the measurement of space-like distances to the measurement of causal intervals in the World with a special (cone) structure |
| | | D. The structure of field supermatrix U and of equation (2) of the causal proximity algebra |
| | 3. Corollaries |
| | Acknowledgements |
| | References |
| II. Group Decomposition in the Special Grand Unification Model in High Energy Physics (S. Ganebnykh, G. Stavraki) |
| | 1. Introduction |
| | | A. Symmetry in grand unified models in particle physics |
| | | B. Brief description of the special grand unification model (à detailed account see I). Necessity of work with high-dimensional representations of the symmetry group E6 |
| | 2. Algorithm of decomposition of tensor products of E6 representations |
| | | A. The set of E6 roots and the corresponding split Lie algebra, the set of Weyl group generators, the representation weight multiplicities, and dimension formula |
| | | B. Algorithm of finding the basis representations of a decomposition of the tensor product of E6 algebra representations. Beginning of the computations of the corresponding multiplicities: stage 1 -- the Weyl group construction |
| | | C. Stage 2 of multiplicity calculation by formula (16): construction of arrays of vector values of the argument of the partition function P |
| | | D. Stage 3: Evaluation of the partition function P in formula (16) |
| | | E. Final stage: direct multiplicity computation by the Kostant formula (16) |
| | | F. Results |
| | | G. Notes |
| | 3. Algorithm of decomposition of E6 representations into D5 subalgebra representations |
| | | A. Singling out D5 subalgebra in the algebra E6:
splitting the root set and the basis set of algebra generators, and singling out a special generator corresponding to the U(1) group degree of freedom |
| | | B. Weyl group and dimensional formula for D5 algebra |
| | | C. Comparative description of the algorithms (based on formula (12)) for computation of representation weight multiplicities in E6, D5, and A4 algebras |
| | | D. Formulas of going over from E6 to D5 weights in the description of multiplets |
| | | E. Description of E6 multiplet decomposition into D5 representations |
| | | F. Results |
| | | G. Possible physical applications: the first hypothetic superselection rule |
| | 4. Algorithm of decomposition of D5 representations into A4 representations |
| | | A. Selection of the A4 subalgebra in the subalgebra D5 Ì E6 |
| | | B. Weyl group and dimensional formula for the A4 algebra |
| | | C. Formulas of transition from D5- to A4-weights
in the description of multiplets |
| | | D. D5 multiplet decomposition into A4 representations |
| | | E. Results |
| | | F. Possible physical applications: the second hypothetical superselection rule |
| | 5. Conclusion. Specific prediction of the model |
| | Acknowledgements |
| | Appendix A |
| | Appendix B |
| | References |
Stavraki George L.
Theoretical physicist, currently researcher, Federal Research Center “Computer Science and Control”, Russian Academy of Sciences. In 1966 his report on the International school on high energy physics (Yalta) suggested the possibility of local descriptions of a system of interacting boson and fermion fields within the framework of a unified closed algebra that generalizes the canonical commutation relations, and was the first to define the concept of Lie superalgebras (referred to as K-algebras) and to construct an example of a simple Lie superalgebra. In 1990 the “Theoretical and mathematical physics” journal published his first version of the operator-field model of space-time as a virtual causal structure. In 2009 he published a book, “Model of Space-Time as a Field Noncommutative Causal Structure” (M.: URSS) detailing the construction of the model and giving consequences that determine the characteristics of the group charge of its basic fields.
