Viktor Redkov (B.I. Stepanov Institute of Physics, Minsk, Belarus)

On parametrization of the finite transformations of the unitary group SU(4)

The Dirac matrix basis is taken to construct the theory of the unitary group SU(4). Parametrization of finit matrices G of the complex linear group GL(4,C) in terms of four complex vector-parameters G=G(k,m,n,l) is proposed and investigated. Additional restrictions separating some sub-groups of GL(4,C) are given explicitly. In the given parametrization, the problem of inverting any matrix G is solved. Expression for determinant of G is found: det G = F(k,m,n,l). Unitarity conditions in the theory on SU(4) group on the base of complex vector parametrization are investigated. Unitarity conditions have been formulated in the form of non-linear cubic algebraic equations for 16 complex-valued pavariables. Several simplest types of solutions have been constructed: 1-parametric Abelian sub-group; three 2-parametric sub-groups ; one 4-parametric unitary sub-group. Curvilinear coordinates to cover these sub-groups have been found.

Joint work with A.A. Bogush and N.G. Tokarevskaya (B.I. Stepanov Institute of Physics, Minsk, Belarus).