- #1
Elwin.Martin
- 207
- 0
I feel kind of lame, but here's my situation:
We start with the operator [itex]g_{\mu \nu} \Box - \partial_{\mu}\partial_{\nu}[/itex] and convert to momentum space to get [itex]-g_{\mu \nu} k^{2} - k_{\mu}k_{\nu}[/itex].
Apparently it's easy to see that this has no inverse?
I'm told that if it *did* it would be of the form
[itex]Ag^{\nu \lambda} +B k^{\nu}k^{\lambda}[/itex]
but I don't see why it would be in this form, to start with. Are these A's and B's just constant coefficients...?
I understand that given the form above, we can simply multiply our inverse and original operator and we get that [itex]-Ak^{2}\delta_{\mu}^{\lambda} +A k_{\mu}k^{\lambda}=\delta_{\mu}^{\lambda}[/itex]
. . . but I don't see why this is an issue, or rather, I can't see why this equation has no solution.
Thanks for any and all help,
E_Martin
We start with the operator [itex]g_{\mu \nu} \Box - \partial_{\mu}\partial_{\nu}[/itex] and convert to momentum space to get [itex]-g_{\mu \nu} k^{2} - k_{\mu}k_{\nu}[/itex].
Apparently it's easy to see that this has no inverse?
I'm told that if it *did* it would be of the form
[itex]Ag^{\nu \lambda} +B k^{\nu}k^{\lambda}[/itex]
but I don't see why it would be in this form, to start with. Are these A's and B's just constant coefficients...?
I understand that given the form above, we can simply multiply our inverse and original operator and we get that [itex]-Ak^{2}\delta_{\mu}^{\lambda} +A k_{\mu}k^{\lambda}=\delta_{\mu}^{\lambda}[/itex]
. . . but I don't see why this is an issue, or rather, I can't see why this equation has no solution.
Thanks for any and all help,
E_Martin