- #1
LAHLH
- 409
- 1
Hi,
Killing equation in flat space is just [tex] \partial_{\mu}K_{\nu}+\partial_{\nu}K_{\mu}=0 [/tex]. I've seen in various places the solutions to this written as [tex] K^{\mu}=\Lambda^{\mu}_{\nu}x^{\nu}+P^{\mu} [/tex] where P is a constant 4 vector, and [tex]\Lambda_{(\mu\nu)}=0[/tex] (i.e. symmetric part vanishes and it is antisym on lowered components)
Can anyone show me how to derive this equation? does the symmetry at work here somehow relate to the infinitesmial generators of the Lorentz group that one meets in QFT? or does anyone have any good links/books where I could read more about this?
thanks
Killing equation in flat space is just [tex] \partial_{\mu}K_{\nu}+\partial_{\nu}K_{\mu}=0 [/tex]. I've seen in various places the solutions to this written as [tex] K^{\mu}=\Lambda^{\mu}_{\nu}x^{\nu}+P^{\mu} [/tex] where P is a constant 4 vector, and [tex]\Lambda_{(\mu\nu)}=0[/tex] (i.e. symmetric part vanishes and it is antisym on lowered components)
Can anyone show me how to derive this equation? does the symmetry at work here somehow relate to the infinitesmial generators of the Lorentz group that one meets in QFT? or does anyone have any good links/books where I could read more about this?
thanks