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Homework Help: Contraction of a tensor to produce scalar

  1. Dec 1, 2017 #1
    1. The problem statement, all variables and given/known data
    Explain how it is possible to perform a contraction of the tensor
    ##T^{\beta \gamma}_{\delta \epsilon}## in order to produce a scalar T

    2. Relevant equations


    3. The attempt at a solution
    $$T^{\beta \gamma}_{\delta \epsilon}T_{\beta \gamma}^{\delta \epsilon}=T$$

    Not sure if that is correct? Also not used the forums in a while so not sure im using the LaTex correctly here.
     
    Last edited: Dec 1, 2017
  2. jcsd
  3. Dec 1, 2017 #2

    Ray Vickson

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    Science Advisor
    Homework Helper

    You can tell you are not using LaTeX properly, just by reading your own message. For in-line formulas and equations, use "# #" (with no space between the two #s) instead of "$" at the start and end of you object. Also: spell out the actual names of the Greek symbols, so that β is "\beta" (backslash + 'beta'), etc. For your first formula this gives ##T^{\beta \gamma}_{\delta \omicron}## (if the object "ǫ" is an ##\omicron##---I could not figure it out).

    For a displayed formula or equation, just use two $ signs (with no space between them) at the start and the end. That gives
    $$T^{\beta \gamma}_{\delta \omicron}T_{\beta \gamma}^{\delta \omicron} = T$$
    You can right-click on a formula or equation and ask for display as TeX, to see the commands used in the above two examples.
     
  4. Dec 1, 2017 #3
    Thanks Ray, i just edited the equation but cant see why its not displaying correctly? edit: i see now, sorry. Is that correct to say then that the covariant multiplied by the contravariant will reduce it to a scalar?
     
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