Adding alignment marker & gives: Error: Extra }, or forgotten \right \end{align}

Question

I have a weird problem with the Align environment in combination with brackets spanning more than 1 line. When I add alignment markers (&) to my equation in the Align environment I suddenly get an error saying that I have an extra }.

The minimal example that reproduces the error looks like this:

\documentclass[a4paper,10pt]{article}
\usepackage{amsmath}

\begin{document}
    \begin{align}
    J      =& 2  \left[3x \right.  \nonumber  \\
    \left. +& 4  \right]
    \end{align}
\end{document}

If i take out the & it works. If I take out the brackets it also works. Can anyone explain what is going on and how I can overcome this issue?

For completeness, the actual equation looks like this:

\begin{align}
 J=E-\Delta P V =& \gamma\int_{-\pi}^{\pi}\int_0^{r_0}\left[\sqrt{r^2+r^2 \partial_r z^2 + \partial_\phi z^2}-r \cos\theta_Y \right. \nonumber  \\
\left. + & \,\frac{\rho g}{\gamma} z r \left(\frac{z}{2}\cos\alpha-r \sin \alpha \cos\phi\right)-\Delta P r z  \right] dr d\phi
\end{align}

Answer 1

Is that what you want?

% arara: pdflatex

\documentclass{article}
\usepackage{amsmath}

\begin{document}
    \begin{align}
    J &= 2 \left[3x \right. \nonumber \\
     &+ \left. 4  \right]
    \end{align}
\end{document}

The problem in your MWE was that you put a & between your left and right delimiter. Instead of the automatic solution of \left[ and \right] I would recommend a manual choice for most cases (especially here, where the bracket from first line could get another automatic sizing than the bracket from the second line). In the following MWE, you can see how to use \bigl[/\bigr] as an example. In this very case, you could just use [ ], as you do not need enlarged brackets.

% arara: pdflatex

\documentclass{article}
\usepackage{amsmath}

\begin{document}
    \begin{align}
    J &= 2 \bigl[3x \nonumber \\
     &\quad+ 4\bigr]
    \end{align}
\end{document}

And here is your real example:

% arara: pdflatex

\documentclass{article}
\usepackage{amsmath}
\newcommand{\der}{\,\mathrm{d}}

\begin{document}
\begin{align}
J&=E-\Delta PV\nonumber\\
&=\gamma\int_{-\pi}^{\pi}\int_0^{r_0}\biggl[\sqrt{r^2+r^2 \partial_r z^2 + \partial_\phi z^2}-r \cos\theta_Y \nonumber  \\
&\phantom{{}=\gamma\int_{-\pi}^{\pi}\int_0^{r_0}\biggl[}+\frac{\rho g}{\gamma} zr \biggl(\frac{z}{2}\cos\alpha-r \sin \alpha \cos\phi\biggr)-\Delta Prz\biggr] \der r\der\phi
\end{align}
\end{document}

Answer 2

For a split equation like that, I would use multline rather than align:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{multline}
J = E-\Delta P V =
\gamma\int_{-\pi}^{\pi}\int_0^{r_0}\biggl[
  \sqrt{r^2+r^2 \partial_r z^2 + \partial_\phi z^2} - r \cos\theta_Y +{}\\
  \frac{\rho g}{\gamma} z r 
    \left(\frac{z}{2}\cos\alpha- r \sin \alpha \cos\phi\right) -
    \Delta P r z  
\biggr]\,dr \,d\phi
\end{multline}
\end{document}

Note the explicit sizing commands \biggl and \biggr that are unavoidable if the delimiters are in different parts of a display (including different cells in a single row of align).

If you prefer a three stage display, use split:

\documentclass{article}
\usepackage[tbtags]{amsmath}
\begin{document}

\begin{equation}
\begin{split}
J &= E-\Delta P V\\
&= \gamma\int_{-\pi}^{\pi}\int_0^{r_0}\biggl[
     \sqrt{r^2+r^2 \partial_r z^2 + \partial_\phi z^2} - r \cos\theta_Y +{}\\
&\hspace{6em}\frac{\rho g}{\gamma} z r
     \left(\frac{z}{2}\cos\alpha- r \sin \alpha \cos\phi\right) -
     \Delta P r z
\biggr]\,dr \,d\phi
\end{split}
\end{equation}

\end{document}

The \hspace{6em} bit has been computed by eye; with a \hphantom you can add the precise space for aligning to something in the line above, although it doesn't seem necessary.

Answer 3

\documentclass[a4paper,10pt]{article}
\usepackage{amsmath}

\begin{document}
    \begin{align}
    J      &= 2  \left[3x \right.  \nonumber  \\
     & \left.{}+ 4  \right]
    \end{align}
\end{document}

1. In your example the pair \left \right was separated by &, not being a group.

2. Please observe the switch of & and =.

3. Using the group left and right is easy, but not recommended. In particular the effective sizes of parentheses may be different in different lines.

4. I would rather add, e.g., \quad before + in the second line.