  Applications of the Dirac equation with an anomalous magnetic moment are
considered for description of characteristics of electrons, muons and quarks.
The Dirac equation with four-dimensional scalar and vector potentials is
reduced to a form suitable for a numerical integration. When a certain type of
the potential is chosen, solutions can approximate quark states inside hadrons.
In view of complicated behaviour of quarks in a confinement domain some
generalizations are considered such as the Dirac-Gursey-Lee equation, the Dirac
equation in a five-dimensional Minkowski space, the Dirac equation in a quantum
phase space. Extended symmetries for the Dirac equation and its generalizations
are considered, which can be used for investigation of properties of solutions
of these equations and subsequent applications in particle physics.
