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L=-[itex]\frac{1}{4}[/itex]F_{ab}F^{ab}

Then the stress-energy tensor is given by:

T^{mn}=-F^{ml}∂^{v}A_{l}+[itex]\frac{1}{4}[/itex]g^{mn}F_{ab}F^{ab}

The author then redefines T^{mn}- he adds ∂_{l}Ω^{lmn}to it,

where Ω^{lmn}=-Ω^{mln}.

The redefined tensor is:

T^{mn}=-F^{m}_{l}F^{vl}+g^{mv}[itex]\frac{1}{4}[/itex]F_{ab}F^{ab}

It is gauge invariant and still satisfies ∂_{m}T^{mn}=0.

The question: is why the addition is allowed? - to my uneducated mind the procedure seems like changing the energy-momentum tensor arbitrarily.

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# Gauge invariance of stress-energy tensor for EM field

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