# How should Christoffel symbols be written (in LaTeX)? [closed]

I'm writing a summary of a lecture on relativity, and we've recently introduced the Christoffel symbols. It seems that the upstairs indices are the "leftmost" and the downstairs indices are somewhat right-aligned, at least in print. I found this way of writing them in several works of literature as well as on Wikipedia. My question thus is:

Should I write $$\Gamma^\mu_{\beta\alpha}$$

using

\Gamma^{\mu}_{\beta\alpha}

or $$\Gamma^{\mu}_{\hphantom{\mu}\beta\alpha}$$

using

\Gamma^{\mu}_{\hphantom{\mu}\beta\alpha}

or does it simply not matter that much?

Of course, the second way can be done more elegantly with a \newcommand

\newcommand{\christoffel}[2]{\Gamma^{#1}_{\hphantom{#1}#2}}

I know this is more of a LaTeX question, but I guess physicists know more about the core of the question than TeX-perts.

• I'd prefer the later one, with a separation under the $\mu$. This also gives you the option to raise and lower the indexes in a natural manner, should you need it. – Mikael Fremling Jan 14 '16 at 17:22
• I'm voting to close this question as off-topic because 1. Christoffel symbols are not a "physical" quantity (they also appear in pure differential geometry) and 2. questions "What is the standard notation for this quantity" are off-topic. – ACuriousMind Jan 14 '16 at 17:32
• There is the "tensor" package, but I think it gave some spacing problems. – jinawee Jan 14 '16 at 17:58
• I'm voting to close this question as off-topic because there are probably a lot of physicist on the TeX stackexchange (also, this is a typographical question), so this should go there. – Martin Jan 14 '16 at 20:33

Horizontal position of indices matters in principle because one might want to raise and lower indices on the Christoffel symbols. If the horizontal position of indices are not observed in a consistent manner, it becomes ambiguous which index was raised or lowered, and so forth, in particular if the connection is not torsionfree. Also note that different authors use different notations and horizontal orderings, e.g. $\Gamma^{\mu}{}_{\alpha\beta}$ vs. $\Gamma_{\alpha\beta}{}^{\mu}$.
• Right. Most authors probably do use $\Gamma^\mu_{\alpha\beta}$ and if they ever use any form with differently raised or lowered indices, they do follow particular conventions about the ordering of the indices. Whenever the indices are not "1 index above a pair of 2", then it must be explained what is the relationship with the normal form of the symbol. – Luboš Motl Jan 14 '16 at 17:55