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Qmechanic ♦
Qmechanic ♦
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Is the correct way to lorentzLorentz transform a tensor T$T$ by writing $\Lambda T \Lambda^T$ or $\Lambda^T T \Lambda$?

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Mikkel Rev
Mikkel Rev
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Is the correct way to lorentz transform a tensor T by writing $\Lambda T \lambda^T$\Lambda^T$ or $\Lambda^T T \Lambda$?

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Mikkel Rev
Mikkel Rev
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Is the correct way to lorentz transform a tensor T by writing $\Lambda T \lambda^T$ or $\Lambda^T T \Lambda$?

Is the correct way to Lorentz transform a tensor T by writing $\Lambda T \Lambda^T$ or $\Lambda^T T \Lambda$? Is it ${\Lambda_\rho}^\mu{\Lambda_\sigma}^\nu T_{\mu \nu}$ or ${\Lambda^\mu}_\rho{\Lambda^\nu}_\sigma T_{\mu \nu}$? MTW adopts ${\Lambda^\mu}_\rho{\Lambda^\nu}_\sigma T_{\mu \nu}$ on page 439, however some lecture notes (page 5 of http://web.phys.ntnu.no/~mika/week10.pdf) uses ${\Lambda_\rho}^\mu{\Lambda_\sigma}^\nu T_{\mu \nu}$. This makes we worried that I have misunderstood everything with regards to suffix notation. Which of these are correct? Or are both correct? If so, why?