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Having stated the behaviour of the covariant derivatives in respect of the variations caused by an infinitesimal coordinate transformation, we obtain a simple expression of the energy-momentum tensor for a field defined, in a riemannian space-time, by a second-rank antisymmetric tensor. A field defined by a second-rank symmetric spinor and by his complex conjugate, in a riemannian space-time, is then considered and, by the invariance of the action for a general infinitesimal coordinate transformation...
In the flat space-time referred to Galileian coordinates, we derive - in this first paper - the expression of the symmetric total energy-momentum tensor, and connected conservation laws, for a field defined by a second-rank antisymmetric tensor, depending on two potential vectors. In particular, for the free electromagnetic field in vacuo, we get the energy-momentum tensor expressed by the irrotational and the solenoidal part of the electromagnetic tensor.
In the flat space-time referred to Galileian coordinates, we derive - in this second paper - the expression of the total energy-momentum spinor, and connected conservation laws in spinor form, for a field defined by a second-rank symmetric spinor and by its complex conjugate. In particular, for the free electromagnetic field in vacuo, we get the energy-momentum spinor expressed by the two parts of the electromagnetic spinor depending on the hermitian part and on the anti-hermitian one of the potential...
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