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Symmetric energy-momentum tensor: the Abraham form and the explicitly covariant formula | | V.V. Nesterenko
; A.V. Nesterenko
; | | Date: |
21 Apr 2015 | | Abstract: | We compare the explicitly covariant 4-dimensional formula, recently proposed
by V.P. Makarov and S.A. Rukhadze [Phys. Usp. {f 52} 937 (2011)] for
symmetric energy-momentum tensor of electromagnetic field in a medium, and the
energy-momentum tensor derived by Abraham in the 3-dimensional vector form. It
is shown that these two objects coincide only on the physical configuration
space $overline Gamma $, formed by the field vectors and the velocity of the
medium, which satisfy the constitutive relations. It should be emphasized that
the 3-dimensional vector formulae for the components of the energy-momentum
tensor were obtained by Abraham only on $overline Gamma $, and the task of
their extension to the whole unconditional configuration space $Gamma$ was not
posed. In order to accomplish the comparison noted above we derive the
Makarov-Rukhadze formula a new by another method, namely, by generalizing the
Abraham reasoning. The comparison conducted enables one to treat the
Makarov-Rukhadze formula as a unique consistent extension of the Abraham
formulae to the whole configuration space $Gamma$. Thus the question
concerning the relativistic covariance of the original 3-dimensional Abraham
formulae defined on $overlineGamma$ is solved positively. We discuss in
detail the relativistic covariance of the 3-dimensional vector formulae for
individual components of the 4-dimensional tensors in electrodynamics which is
manifested in the form-invariance of these formulae under Lorentz
transformations. | | Source: | arXiv, 1504.5518 | | Services: | Forum | Review | PDF | Favorites | |
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