I have sent one question about the Lorentz transformation of M and P without explaining enough the reason of doing it. Therefore let me to come back to such question made in more accurate physical form.
The electric or magnetic susceptibilities are physical dimensionless measurable magnitudes, i.e. they are pure numbers and thus they would be invariant for every possible group where M,H or P,E might transform. In our case we could think in the Lorentz group and suppose two inertial observers moving with a relativistic relative velocity measuring the same susceptibility of the material. For instance, if we have a magnetic material, the magnetic field of the denominator must tranform in the usual form introducing introducing a new electric term: is going to do the same the magnetization M?. In what form? And the same could be done for electric susceptibility. What are them the Lorentz transformations of M and P?
All these questions can help to understand the differences of H,M and B which were asked in another question that I have tried to answer.
This is a non-trivial problem, but has been intensely studied in the past in the context of electrodynamics of moving media as pioneered by the great Arnold Sommerfeld. I recommend Sommerfeld's book "Electrodynamics". Have also a look to the paper "A study of electrodynamics of moving media" by C.T. Tai , Proceedings of the IEEE, page 685 (1964).
Dear Christian,
Thank you very much for your answer, although I am not agree with your recommendation with respect to the book of Arnold Sommerfeld as a good reference ,nowadays, for this question for several reasons:
1. The electric magnitudes are well defined as tensors, but the magnetic ones do not follow the usual ones used nowadays in the first chapter. In chapter four recovers the usual ones when he works with the model of Minkowski.
2. The model of Minkowski also works with one euclidean metric using a complex time but this makes also to represent the tensors into a field of numbers quite difficult to understand, i,e, with complex and real physical magnitudes in the same footing of measurements.
3. In no place the electromagnetic magnitudes are transformed as Lorentz tensors keeping their associated invariants.
Please, could you attach the IEEE paper that you suggest as a good reference? Thank you.
Thank you very much and let me to attach you a paper with the geometrical meaning of what I want to say.
Dear Christian,
Thank you very much for your papers which are very interesting indeed and they work on the constitutive relations of electrodynamics in many different forms, although a general solution of Lorentz tensors is not found. This is a very difficult question which is far of being studied, in all that I know.
The question in its more simple form is the following: you have easily Lorentz transformations for E and H, B and D or J or Ro, but what happens with the tranformations of M and P? Are they tensors? Lorentz tensors?
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