The triality properties of Dirac spinors are studied, including a construction of the algebra of (complexified) biquaternion. It is proved that there exists a vector-representation of Dirac spinors. The massive Dirac equation in the vector-representation is actually self-dual. The Dirac’s idea of non-integrable phases is used to study the behavior of massive term.

We define the Dirac-Fock current to hold the current conservation in the momentumdependent Dirac fields, and discuss its effect on the magnetic-moment in the nuclear matter. It is shown that the Dirac-Fock current can largely reduce the magneticmoment even in the isovector case, whose value has been too big due to the small effective mass in the usual relativistic Hartree approximation.

Dirac deformation of Poisson operators of arbitrary rank is considered. The question when Dirac reduction does not destroy linear Poisson pencils is studied. A class of separability preserving Dirac reductions in the corresponding quasi-bi-Hamiltonian systems of Benenti type is discussed. Two examples of such reductions are given. This paper will appear in J. Phys. A: Math. Gen. AMS 2000 Subjec...