Energy and momentum in classical electrodynamics

4 Energy and momentum of the coupled fields 10.4.1 Energy and momentum in classical electrodynamics 

The energy-momentum tensor derived from Noether s theorem for electrodynamics 

Energy-momentum conservation is expressed by dvT = 0 for a closed system. If Tfi were a symmetric tensor (when converted to 7 /x ), this would be assured because i f Tfi = 0 by construction. Since the gauge field part of the tensor deduced from Noether s theorem is not symmetric, this requires special consideration, as discussed below. A symmetric energy-momentum tensor is required for any eventual unification of quantum field theory and general relativity [422], The fermion field energy and momentum are 

E(fir) = j d x fifi, P(i/0 = j where, for a massless electron of negative helicity (positive energy), 

For the Maxwell field, the energy-momentum tensor Tfi(A) derived from Noether s theorem is unsymmetric, and not gauge invariant, in contrast to the symmetric stress tensor derived directly from Maxwell s equations [318], Consider the symmetric tensor 0 = T + AT, where 

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