The definitions of the auxiliary fields are: D ( r , t ) = ε ε 0 E ( r , t ) + P ( r , t ) , H ( r , t ) = 1 μ μ 0 B ( r , t ) − − M ( r , t ) , where P is the polarization field and M is the magnetization field, which are defined in terms of microscopic bound charges and bound currents respectively. The macroscopic bound charge density ρ b and bound current density J b in terms of polarization P and magnetization M are then defined as ρ ρ b = − − ∇ ∇ ⋅ ⋅ P , J b = ∇ ∇ × × M + ∂ ∂ P ∂ ∂ t .