Dual field tensor

Property 2. If two scalar fields <[), 0 form an arbitrary pair of dual fields, in the sense of Eq. (15) [or, equivalently, if they verify (119)], the tensors Fap and F.jfi satisfy the Maxwell equations in empty space at any time. 

In terms of the dual field strength tensor the homogeneous Maxwell equations... 

In utilizing a complex three-vector (self-dual tensor) rather than a real antisymmetric tensor to describe the electromagnetic field, Hillion and Quinnez discussed the equivalence between the 2-spinor field and the complex electromagnetic field [63]. Using a Hertz potential [64] instead of the standard 4-vector potential in this model, they derived an energy momentum tensor out of which Beltrami-type field relations emerged. This development proceeded from the Maxwell equations in free homogeneous isotropic space... 

Theorem. Let k be a field, G a closed subgroup of GL . Every finitedimensional representation of G can be constructed from its original representation on fc" by the processes of forming tensor products, direct sums, subrepresentations, quotients, and duals. 

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