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Evaluating contractions of a tensor product

  1. Feb 4, 2015 #1

    CAF123

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    1. The problem statement, all variables and given/known data
    Consider ##T = \delta \otimes \gamma## where ##\delta## is the ##(1,1)## Kronecker delta tensor and ##\gamma \in T_p^*(M)##. Evaluate all possible contractions of ##T##.

    2. Relevant equations

    Tensor product


    3. The attempt at a solution

    ##\gamma## is therefore a ##(0,1)## tensor and the tensor product with ##(1,1)## yields a ##(1,2)## tensor. The components of ##T## are therefore ##T^a_{\,\,\,\,\,bc}## which gives rise to the two possible contractions ##T^a_{\,\,\,\,\,ab}## or ##T^a_{\,\,\,\,\,ba}##. Do I need to include any more detail? Thanks.
     
  2. jcsd
  3. Feb 5, 2015 #2

    Orodruin

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    I would say you also need to evaluate what these contractions actually are in terms of ##\gamma## and ##\delta##.
     
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