Evaluating contractions of a tensor product

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  • #1
CAF123
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Homework Statement


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##.

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Tensor product


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.
 

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  • #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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