Projection operators and the transverse electrical-conductivity tensor of a material system

Starting from a hamiltonian describing nonrelativistic charged particles with spin, the conventional linear response theory to obtain the conductivity tensor of a many-body system is reviewed. A projection operator is then defined which yields the correct expression for the transverse part of the conductivity tensor in terms of the transverse part of a current-current commutator correlation function with a modified propagator. Furthermore one can show that a second projection operator may be defined which yields the transverse part of the impedance for transverse normal waves. The difficulties are discussed which arise if one attempts to derive an analogous expression for the longitudinal conductivity.