# Lie Algebra of the Lorentz group - a weird notation?

1. Dec 13, 2014

### Theage

In Srednicki's text on quantum field theory, he has a chapter on quantum Lorentz invariance. He presents the commutation relations between the generators of the Lorentz group (equation 2.16) as follows:
$$[M^{\mu\nu},M^{\rho\sigma}] = i\hbar\Big(g^{\mu\rho}M^{\nu\sigma}-(\mu\leftrightarrow\nu)\Big)-(\rho\leftrightarrow\sigma)$$
I have never seen the strange double-arrow notation in any linear algebra book before. Is this notation at all standard and if so, what does it mean?

2. Dec 13, 2014

### ShayanJ

It just means "its the same thing as the last term, just put $\mu$ instead of $\nu$ and vice-versa." The same about the last parenthesis.

3. Dec 13, 2014

### haushofer

Indeed. The lhs should be antisymm. in mu and nu, and also in rho and sigma. That's what this notation says :)

4. Dec 13, 2014

### dextercioby

A typographical convenience, nothing more. Weinberg for instance makes no LaTex shortenings.