- The first publications (from my postgraduated student age) are connected with strings, space-time-field symmetry (idea of M.Kõiv) and with the equations of the gauge fields. Last ones assumed as real carriers of fundamental forces : electromagnetic, weak and strong interactions. The group analysis, developed by S.Lie, A.Bäcklund and others, proved as a good tool for investigation corresponding equations. It appears that the well-known gauge transformations are the Lie-Backlund transformations also.
- Second subject of my investigations is connected with the quantum-mechanical restrictions of physical measurement. Expression of the minimal shift of the interference pattern of the electrons in the magnetic field deduced. This have methodological value only.
- The Standard Model of elementary particles and their interactions, developed by S.-L.Glashow,A.Salam,S.Weinberg and others is a good phenomenological theory, but there are many undetermined constatnts and so we are not able to determine the masses of fermions. Also there are not any good explanation of the three generations of particles. For "our world" enough of the first one ( Who orders others?). At last, there is a puzzling hypotetical Higgs boson in the common theory, which is nondetected on the particle accelerators so far. These are well-known problems for specialists.
IMHO, there are some reasons to assume that the well-known Kemmer-Duffin-Petiau equations may be useful thing for generalize the Standard Model. But so far only some special cases of these equations and corresponding -matrices used. We computed general expressions of these 16x16 matrices, using the computer software Maple. Interesting results was published by Andrzej Okninski recently, but he uses the special cases of these -matrices also.
The computer-algebra softwares, such as above mentioned Maple, also Mathematica, MatLab, REDUCE and etc. are very useful tools for physic theorists.For example, there are special packets also:
- HIP - Symbolic High-Energy Physics Calculations, especially for Feynman diagrams. Both, Mathematica and Maple variants (E.Yehudai, FNAL, USA )
- GRTensorII - for gravitation tensor-calculations. Both, Maple and Mathematica variants (Queen's University, Kingston, Canada)
- CLIFF2 - Clifford algebra for Maple (R. Ablamowicz, Gannon University)