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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 $I^{\mu\nu}$?

  • 1
    Is this correct? I don't see the index $\mu$. – 2017-02-20
  • 0
    question edited to take into account your comment – 2017-02-20

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