Question About Calculation in Maggiore's Quantum Field Theory

[PJK]

I have a question about an equation in Maggiore's Modern Introd. to Quantum Field Theory p.52:
$$\delta x^\mu = w^\mu_\nu x^\mu = \sum_{\rho < \sigma} A^\mu_{(\rho \sigma)} w^{\rho \sigma}$$
where the A is defined as
$$A^\mu_{(\rho \sigma)}=\delta^{\mu}_{\rho}x_\sigma - \delta^\mu_\sigma x_\rho$$

If I do this calculation I always end up with a factor 3 on the right hand side times the desired result. Is this an error in the book? Or am I doing something wrong?

 

[RedX]

The author is correct. Usually 'Aw' is written as '1/2 Aw' without specification that one indice is smaller than the other (A and w are antisymmetric so this is possible).

It's a bit baffling that the author defines the rotations like that though. I think the x's in the definition of A should be replaced by the metric 'g' that contracts with 'x' to get those expressions. That way iA would be a generator for the SO(4) vectorial representation.