# Evaluating contractions of a tensor product

1. Feb 4, 2015

### CAF123

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. Feb 5, 2015

### Orodruin

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