RELATIVISTIC ENERGY-MOMENTUM TENSOR IN POLARIZED MEDIA .3. STATISTICAL THEORY OF ENERGY-MOMENTUM LAWS

From the atomic conservation laws of energy-momentum the corresponding macroscopic laws are derived with the help of a covariant averaging procedure. The total energy-momentum tensor is found as a statistical expression in terms of atomic quantities. It may be split into a field part Tαβ({cauchy integral}) (α, β = 0, 1, 2, 3) containing the macroscopic fields and polarizations, which in the rest frame reads: Tαβ({cauchy integral}) = 1 2E2+ 1 2B2 (E ∧ H)i (E∧H)i -EiDj-HiBj+( 1 2E2+ 1 2B2-M{dot operator}B)gij(i,j =1,2,3)and a material part Tαβ(m) which forms the relativistic generalization of the usual energy and momentum expressions. © 1968.