- #1
vnikoofard
- 12
- 0
Hi Friends
I am reading the following paper
http://arxiv.org/abs/hep-th/9705122
In the page 4 he says that
[itex]\tilde{W}_{\mu\nu}=0\Rightarrow V_{\mu}=\partial_{\mu}\lambda[/itex]
Where [itex]\tilde{W}^{\mu\nu}\equiv\frac{1}{2}\epsilon^{\mu \nu\rho\sigma}W_{\rho\sigma}[/itex] and [itex]W_{\mu\nu}\equiv\partial_{[\mu}V_{\nu]} [/itex] and [itex] \epsilon [/itex] is antisymmetric Levi-Civita tensor.
The above expression is a general argument and it is not related to the paper. I can not understand how can we drive [itex]V_{\mu}=\partial_{\mu}\lambda[/itex] from [itex]\tilde{W}_{\mu\nu}=0 [/itex]
Would someone please explain it for me
I am reading the following paper
http://arxiv.org/abs/hep-th/9705122
In the page 4 he says that
[itex]\tilde{W}_{\mu\nu}=0\Rightarrow V_{\mu}=\partial_{\mu}\lambda[/itex]
Where [itex]\tilde{W}^{\mu\nu}\equiv\frac{1}{2}\epsilon^{\mu \nu\rho\sigma}W_{\rho\sigma}[/itex] and [itex]W_{\mu\nu}\equiv\partial_{[\mu}V_{\nu]} [/itex] and [itex] \epsilon [/itex] is antisymmetric Levi-Civita tensor.
The above expression is a general argument and it is not related to the paper. I can not understand how can we drive [itex]V_{\mu}=\partial_{\mu}\lambda[/itex] from [itex]\tilde{W}_{\mu\nu}=0 [/itex]
Would someone please explain it for me