Recently a article published in http://physics.aps.org/articles/v8/2 , says that imaginary magnetic are experimentally verified in lab and they are not only mathematical outcomes.
Electromagnetic tensor( http://en.wikipedia.org/wiki/Electromagnetic_tensor) is a mathematical object that describes the electromagnetic field of a physical system.
When you see this tensor it only covers the real values of electric and magnetic field.
My question is do electromagnetic tensors fail to explain imaginary components of electric and magnetic field?
Nothing forbids that the field tensor be complex, yet the potential must be complex too.
Hello Claude Pierre Massé,
If we replace real components with complex component (Potentials) will it be good enough or we will have to make some adjustment in original tensor?
Regards,
Bhushan Poojary
Dear Bhushan,
The tensor electromagnetic field is defined in vacuum and no in materials or physical phases as can be ferromagnetism. Thus it is no sense to introduce this complex components in the antisymmetric 2- Lorentz tensor associated to the electromagnetic field. The reason is that it is not going to follow the follow Lorentz transformations SO(3,1)
From the ciation http://en.wikipedia.org/wiki/Skew-symmetric_matrix:
"From the spectral theorem, for a real skew-symmetric matrix (antisymmetric) the nonzero eigenvalues are all pure imaginary and thus are of the form iλ1, −iλ1, iλ2, −iλ2, … where each of the λk are real". A unitary transformation, such like the Lorentz transformation in Minkowski space, can be represented through a complex matrix, this makes possible to obtain the diagonalized field tensor in some special coordinate system (see the special relativity theory). Therefore, some complicated (and complex) relationship between the electric anf magnetic field components in "their own reference" frame and in the new reference frame can exist.
Furthermore, the Gauss's law and Ampère's circuital law can be written through the system of the differential equations for the field tensor F^{\alpha\beta} components:
\partial_{\alpha} F^{\alpha\beta} = \mu_0 J^{\beta},
where J^{\beta} is 4-current.
Hence, in general, the solution of the system of the differetial equations can contain complex exponents or items. The corresponding values of the electric and magnetic fields can be deceying and/or oscillating depending on the task condition. The last can be expressed thorugh some complex variables. However, we can measure only real quantities. Hence, the comlex values can just formally reflect some quality of the processes. But, at the same time, the nature and properties of the processes should not change from one reference to another in accordance with the special relativity concepts.
My remarks were linked with Lorentz tensors and no with antisymmetric matrices or their eigenvalues. The question is that if you want to put something forming part of the electromagnetic field then you need to make be able to tranform it as a Lorentz tensor.
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