1

I am struggling to derive the relations on the right hand column of eq.(4) in https://arxiv.org/pdf/1008.4884.pdf

Even the easy abelian one (third row)

which is

$D_\rho B_{\mu\nu}=\partial_\rho B_{\mu\nu}$

doesn't match my calculation

Since

$D_\rho B_{\mu\nu}=(\partial_\rho+i g B_\rho)(\partial_\mu B_\nu-\partial_\nu B_\mu)$

the equation seems to imply that

$B_\rho (\partial_\mu B_\nu-\partial_\nu B_\mu)=0$

What am I missing?

d8586
  • 31
  • The $U(1)$ covariant derivative is $D_\mu = \partial_\mu + i g Q B_\mu$ where $Q$ is the charge of the field on which it is acting. Here, it is acting on $B_{\mu\nu}$ which is neutral so $Q=0$. – Prahar Jan 05 '17 at 14:36

0 Answers0