Fermionic fields in six-dimensional space-time

The Dirac equation in six-dimensional space-time has been derived which yields the exact equation of continuity. The Dirac matrices obey the complete Dirac algebra in such space, the sixtyfour elements of which satisfy the same properties as satisfied by the usual Dirac matrices in four-dimensional space-time. The relativistic invariance of Dirac equation has been demonstrated under different types of Lorentz transformations. The plane wave solutions of Dirac equation are obtained which result in two types of spinors subject to different conditions on the energy and momentum components. The reduction and second quantization of Dirac field has been carried out and the fermion propagator has been constructed in such space. The Lagrangian formulation of Dirac field has also been carried out in terms of annihilation and creation operators in six-dimensional space. (author). 19 refs