# Aligning multiple lines in long equations and arranging the line breaks in \align environment

I have the following code sample:

\begin{align}
\pi^{(1)}_{i j} \enspace & = \enspace -\frac{1}{4}\eta^{\lambda \sigma} \left( \eta^{\mu \alpha}\eta^{\nu \beta} + \eta^{\mu \beta}\eta^{\nu \alpha}  \right) \biggl\{ \frac{1}{2}\delta_{\lambda 0}( \delta_{\mu i}\delta_{\nu j} + \delta_{\mu j}\delta_{\nu i}  )   \biggr\} \partial_{\sigma} h_{\alpha \beta}
\nonumber
\\
-\frac{1}{4}\eta^{\lambda \sigma} \left( \eta^{\mu \alpha}\eta^{\nu \beta} + \eta^{\mu \beta}\eta^{\nu \alpha}  \right) \biggl\{ \frac{1}{2}\delta_{\sigma 0}( \delta_{\alpha i}\delta_{\beta j} + \delta_{\alpha j}\delta_{\beta i} )  \biggr\} \partial_{\lambda} h_{\mu \nu}
\mspace{-458mu}
\nonumber
\\
& = \enspace -\frac{1}{4}\partial^{\lambda} h^{\mu \nu}\delta_{\lambda 0}( \delta_{\mu i}\delta_{\nu j} + \delta_{\mu j}\delta_{\nu i} ) -\frac{1}{4}\partial^{\sigma} h^{\alpha \beta}\delta_{\sigma 0}( \delta_{\alpha i}\delta_{\beta j} + \delta_{\alpha j}\delta_{\beta i} )
\nonumber
\\
& = \enspace -\frac{1}{2}\partial^0 h^{i j} - \frac{1}{2}\partial^0 h^{i j}
\nonumber
\\
& = \enspace \dot{h}_{i j}
\end{align}


which gives the output:

As you see, I have a problem in aligning the lines properly which I tried to handle by using \mspace{}. My first question is: What is the correct or proper way of doing this in these kind of lengthy equations?

I also have another problem. When I use separate \align environments repeatedly, at some moment I reach to the end of the page and the last \align environment automatically starts from a new page. In such a case all vertical spaces of the previous page changes and they ruin the proper format of the text. So, my second question is: How to properly arrange line breaks or spacing in repeated \align environments consisting lengthy equations?

You should use split inside equation for this:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

$$\begin{split} \pi^{(1)}_{i j} ={}& -\frac{1}{4}\eta^{\lambda \sigma} ( \eta^{\mu \alpha}\eta^{\nu \beta} + \eta^{\mu \beta}\eta^{\nu \alpha} ) \biggl\{ \frac{1}{2}\delta_{\lambda 0}( \delta_{\mu i}\delta_{\nu j} + \delta_{\mu j}\delta_{\nu i} ) \biggr\} \partial_{\sigma} h_{\alpha \beta} \\ & -\frac{1}{4}\eta^{\lambda \sigma} ( \eta^{\mu \alpha}\eta^{\nu \beta} + \eta^{\mu \beta}\eta^{\nu \alpha} ) \biggl\{ \frac{1}{2}\delta_{\sigma 0}( \delta_{\alpha i}\delta_{\beta j} + \delta_{\alpha j}\delta_{\beta i} ) \biggr\} \partial_{\lambda} h_{\mu \nu} \\ ={}& -\frac{1}{4}\partial^{\lambda} h^{\mu \nu}\delta_{\lambda 0}( \delta_{\mu i}\delta_{\nu j} + \delta_{\mu j}\delta_{\nu i} ) -\frac{1}{4}\partial^{\sigma} h^{\alpha \beta}\delta_{\sigma 0}( \delta_{\alpha i}\delta_{\beta j} + \delta_{\alpha j}\delta_{\beta i} ) \\ ={}& -\frac{1}{2}\partial^0 h^{i j} - \frac{1}{2}\partial^0 h^{i j} \\ ={}& \dot{h}_{i j} \end{split}$$

\end{document}


The trick is to put = on the left side, following it with {} for ensuring correct spacing.

Avoid useless \left and \right. Also, no \enspace should be used around =.

The number should go in the middle, in my opinion. However, the tbtags option to amsmath will put it at the bottom of a split.

• Your answer is very useful, thanks @egreg. I liked the idea of using \split and putting number into the middle and I will use them as the solution to my problem. But, the answer @Harish Kumar gave also works in my case. Since he additionally answers my second question I will accept his answer which I believe (and I hope) is ethically correct. – sahin May 2 '15 at 13:16
• @sahin The additional question is a false problem: you should never have consecutive display environments. Use just one and add \displaybreak before the \\ after which you'd like a break. Use \allowdisplaybreaks only when typing in the document, then decide by eye what are the best break points. – egreg May 2 '15 at 13:19
• In my case, I used the \allowdisplaybreaks locally just before the \align environment that breaks the page and it worked. What are the possible bad consequences of using it like that? In any case, I again liked your suggestion. For a proper look, it could be better to use a single \align as you said. Thanks again. – sahin May 2 '15 at 13:25
• Yeap! Now both of your solutions work for me and my document looks much better. I will change my decision on accepting answers. Thanks. – sahin May 2 '15 at 13:31
• @egreg -- the minus signs that directly follow equal signs should really be unary minuses. they show here as binaries. granted, that would throw off the alignment of the initial fractions ... – barbara beeton May 2 '15 at 15:29

You can add few {} and \phatoms to align.

\documentclass{article}
\usepackage{amsmath}
\allowdisplaybreaks
\begin{document}
\begin{align}
\pi^{(1)}_{i j} & = {}-\frac{1}{4}\eta^{\lambda \sigma} \left( \eta^{\mu \alpha}\eta^{\nu \beta} + \eta^{\mu \beta}\eta^{\nu \alpha}  \right) \biggl\{ \frac{1}{2}\delta_{\lambda 0}( \delta_{\mu i}\delta_{\nu j} + \delta_{\mu j}\delta_{\nu i}  )   \biggr\} \partial_{\sigma} h_{\alpha \beta}
\nonumber
\\
&\phantom{{}={}}{}-\frac{1}{4}\eta^{\lambda \sigma} \left( \eta^{\mu \alpha}\eta^{\nu \beta} + \eta^{\mu \beta}\eta^{\nu \alpha}  \right) \biggl\{ \frac{1}{2}\delta_{\sigma 0}( \delta_{\alpha i}\delta_{\beta j} + \delta_{\alpha j}\delta_{\beta i} )  \biggr\} \partial_{\lambda} h_{\mu \nu}
\nonumber
\\
& = {}-\frac{1}{4}\partial^{\lambda} h^{\mu \nu}\delta_{\lambda 0}( \delta_{\mu i}\delta_{\nu j} + \delta_{\mu j}\delta_{\nu i} ) -\frac{1}{4}\partial^{\sigma} h^{\alpha \beta}\delta_{\sigma 0}( \delta_{\alpha i}\delta_{\beta j} + \delta_{\alpha j}\delta_{\beta i} )
\nonumber
\\
& ={} -\frac{1}{2}\partial^0 h^{i j} - \frac{1}{2}\partial^0 h^{i j}
\nonumber
\\
& ={}\dot{h}_{i j}
\end{align}
\end{document}


For your page breaking problem, use \allowdisplaybreaks.