  The Hamiltonian formulation of the reduced Vlasov-Maxwell equations is
expressed in terms of the macroscopic fields D and H. These macroscopic fields
are themselves expressed in terms of the functional Lie-derivative generated by
the functional S with the Poisson bracket [.,.] for the exact Vlasov-Maxwell
equations. Hence, the polarization vector P= (D-E)/(4pi) and the magnetization
vector M=(B-H)/(4pi) are defined in terms of the expressions 4pi P=[S,E]+...
and 4pi M =-[S,B]+..., where lowest-order terms yield dipole contributions.
