to the applied fields and are called constitutive relations. Determining the constitutive relationship between the auxiliary fields D and H and the E and B fields starts with the definition of the auxiliary fields themselves: where P is the polarization field and M is the magnetization field which are defined in terms of microscopic bound charges and bound current respectively. Before getting to how to calculate M and P it is useful to examine the following special cases. Without magnetic or dielectric materials In the absence of magnetic or dielectric materials, the constitutive relations are simple: where ε0 and μ0 are two universal constants, called the permittivity of free space and permeability of free space, respectively. Isotropic linear materials In an (isotropic) linear material, where P is proportional to E, and M is proportional to B, the constitutive relations are also straightforward. In terms of the polarization P and the magnetization M they are: where χe and χm are the electric and magnetic susceptibilities of a given material respectively. In terms of D and H the constitutive relations are: where ε and μ are constants (which depend on the material), called the permittivity and permeability, respectively, of the material. These are related to the susceptibilities by: General case For real-world materials, the constitutive relations are not linear, except approximately. Calculating the constitutive relations from first principles involves determining how P and M are created from a given E and B. These relations may be empirical (based directly upon measurements), or theoretical (based upon statistical mechanics, transport theory or other tools of condensed matter physics). The detail employed may be macroscopic or microscopic, depending upon the level necessary to the problem under scrutiny. In general, the constitutive relations can usually still be written: but ε and μ are not, in general, simple constants, but rather functions of E, B, position and time, and tensorial in nature. Examples are: As a variation of these examples, in general materials are bianisotropic where D and B depend on both E and H, through the additional coupling constants ξ and ζ: In practice, some materials properties have a negligible impact in particular circumstances, permitting neglect of small effects. For example: optical nonlinearities can be neglected for low field strengths; material dispersion is unimportant when frequency is limited to a narrow bandwidth; material absorption can be neglected for wavelengths for which a material is transparent; and