Maxwell Stress Dyadic in Differential-Form Formalism

摘要

The classical Maxwell stress tensor (or stress-energy-momentum tensor) is211u001erevisited using the formalism of dyadics and differential forms. It is first 211u001eshown that the Lorentz force density must be expressed in terms of a dyadic 211u001emapping trivectors to vectors and, in four-dimensional representation, the 211u001eLorentz force-power density as a mapping from quadrivectors to vectors. The 211u001eexpression of the electromagnetic stress dyadic, or stress-energy-momentum 211u001edyadic, can then be written in particularly simple form in the four-dimensional 211u001erepresentation and the known physical components are seen from its three-211u001edimensional expansion. it is shown that to be able to define the stress dyadic, 211u001ethe macroscopic electromagnetic medium (assumed homogeneous and time independent) 211u001emust satisfy a certain condition which equals the Lorentz condition. The theory 211u001eis based on introduction of a dyadic algebra to differential form formalism as a 211u001emodification of the classical Gibbsian dyadic algebra.