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- W2017693571 abstract "The conservation laws are examined from the transformation properties of the Lagrangian. The energy-momentum complex obtained has mixed indices, ${{T}_{ensuremath{mu}}}^{ensuremath{nu}}$, whereas a symmetric quantity ${mathcal{T}}^{ensuremath{mu}ensuremath{nu}}$ is required for the definition of angular momentum. Such a symmetric quantity has been constructed by Landau and Lifshitz. In the course of examining the relationship between these quantities, two hierarchies of complexes ${{T}_{(n)ensuremath{mu}}}^{ensuremath{nu}}$ and ${{mathcal{T}}_{(n)}}^{ensuremath{mu}ensuremath{nu}}$ are constructed. Under linear coordinate transformations the former are tensor densities of weight ($n+1$) and the latter of weight ($n+2$). For $n=0$ these reduce to the canonical ${{T}_{ensuremath{mu}}}^{ensuremath{nu}}$ and the Landau-Lifshitz ${mathcal{T}}^{ensuremath{mu}ensuremath{nu}}$, respectively.By requiring the energy-momentum complex to generate the coordinate transformations, and the total energy and momentum to form a free vector, one can identify the canonical complex ${{T}_{ensuremath{mu}}}^{ensuremath{nu}}$ as the appropriate quantity to describe the energy and momentum of the field plus matter. Similarly, by requiring the total angular momentum to behave as a free antisymmetric tensor, one can construct, in the usual manner, an appropriate quantity from ${{mathcal{T}}_{(ensuremath{-}1)}}^{ensuremath{mu}ensuremath{nu}}$. The angular momentum complex so defined differs from that proposed by Landau and Lifshitz as well as from an independent construction by Bergmann and Thomson." @default.
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- W2017693571 date "1958-07-01" @default.
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- W2017693571 title "Conservation Laws in General Relativity" @default.
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- W2017693571 doi "https://doi.org/10.1103/physrev.111.315" @default.
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