The project is based on the foundations of the relativistic canonical quantum mechanics for particles of arbitrary mass and spin developed by the author earlier, 64-dimensional matrix representation of Clifford algebra over a field of real numbers in the space of ordinary 4-component Dirac spinors, which significantly expands the possibilities of using Clifford algebras in quantum mechanics and field theory. The extended Foldy–Wouthuysen transformation suggested by author, which relates such quantum mechanical model with the covariant quantum field theory is used as well. We have proved on the basis of these results and principles that the Dirac equation has not only known fermionic but also the bosonic properties. The main achievement is the effective method of synthesis of covariant relativistic equations of motion of elementary particles of arbitrary mass and higher spins, which will be used to solve contemporary problems of particle physics.
Recently new mathematical objects, which are useful for such investigations, were put into consideration. The 256-dimensional representation of the Clifford algebra over the field of real numbers, which is given by 8х8 Dirac gamma matrix, has been suggested. The realizations Cl(0,8) and Cl(1,7) were introduced. Corresponding 45-dimensional gamma matrix representations of the Lie algebras SO(1,9) and SO(10) were considered as well.
On this basis new relativistic wave equations for the particles having spin 3/2 and 2 will be introduced. Such equations will not contain redundant components and additional conditions.
Taking into account that these equations describe particle-antiparticle doublet the application to the problem of particle-antiparticle asymmetry of the Universe is preferable continuation.
|Volodimir Simulik||National Academy of Sciences of Ukraine, Kiev|