Quick Calculation 3.3

A First Course in String Theory

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Verify the equations in (3.26).

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Eq. (3.26):

\displaystyle{ \begin{aligned}   T_{\lambda \mu \nu} &= - T_{\mu \lambda \nu} \\  T_{\lambda \mu \nu} &= - T_{\lambda \nu \mu} \\  \end{aligned} }

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\displaystyle{ \begin{aligned}   T_{\lambda \mu \nu} &=     \partial_\lambda F_{\mu \nu}  + \partial_\mu F_{\nu \lambda}  + \partial_\nu F_{\lambda \mu} \\   \end{aligned} }

\displaystyle{ \begin{aligned}   T_{\mu \lambda \nu}   &= \partial_\mu F_{\lambda \nu}  + \partial_\lambda F_{\nu \mu}  + \partial_\nu F_{\mu \lambda} \\    &=     - \partial_\mu F_{\nu \lambda}  - \partial_\lambda F_{\mu \nu}  - \partial_\nu F_{\lambda \mu} \\    &=     - T_{\lambda \mu \nu} \\      \end{aligned} }

— Me@2022-04-15 05:10:09 PM

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