# Evaluating contractions of a tensor product

Gold Member

## 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##.

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.

Orodruin
Staff Emeritus