# I Deducing the tensorial structure of a tensor

1. Feb 20, 2017

### spaghetti3451

Consider an expression of the following form:

$$I^{\mu\nu}(r) = \int d^{3}k\ \ d^{3}l\ \ \delta^{4}(r-k-l)\ (g^{\mu\nu}k\cdot{l}+k^{\nu}k^{\mu}-k^{\mu}l^{\nu})$$

$I^{\mu\nu}$ must be of the form

$$I^{\mu\nu}(r) = Ar^{\mu}r^{\nu} + B\eta^{\mu\nu},$$

where $A$ and $B$ are constants.

How can you determine this tensorial form of $I^{\mu\nu}$?

Last edited: Feb 20, 2017
2. Feb 25, 2017

### PF_Help_Bot

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