Aligned multiline equations

Question

I'm using an align environment in a long derivation. Each equality is aligned at the equal sign. Individual lines are too long to fit the page, so I need wrap them. However, I don't just want them to continue in the next line as I usually do and maybe indent them with a \quad, I want them to align with the opening bracket which contains all the terms. I've been looking into the aligned environment which sort of does what I want, but now the aligned lines are vertically centered with the beginning of the equality:

\begin{align*}
 Z &= Tr_\text{el, ph}\bigl[\exp(-\beta H)\bigr]\\
 &= \int\mathcal{D}q Tr_\text{el}\biggl[T_\tau\exp\biggl(-\int_0^\beta d\tau\sum_j\Bigl[
 \begin{aligned}
   &-t\sum_\sigma\bigl(c_{j\sigma}^\dag(\tau)c_{j+1,\sigma}(\tau)+\text{h.c.}\bigr)\\
   &+\tfrac{M}{2}\bigl(\dot q_j(\tau)^2+\omega_0^2q_j(\tau)^2\bigr)\\
   &-g\sqrt{2M\omega_0}\sum_\sigma n_{j\sigma}(\tau)q_j(\tau)\Bigr]\biggr)\biggr]
 \end{aligned}\\
 &= ...
\end{align*}

This is what I would like it to look (photoshopped):

I imagine, I'm not the first one to have this problem. I did a thorough search before posting this question, so before you mark this as a duplicate, please consider carefully if the alleged duplicate really addresses my issue.

Answer 1

To get aligned to line up with the first line remember the [t] option.

Don't use \text for anything but textual comments in display math. This _\text{el} is not a textual comment. Better to use another construction.

\documentclass[a4paper]{memoir}
\usepackage{mathtools}
\DeclareMathOperator\Tr{Tr}
% for text only subscripts 
\newcommand\tsub[1]{_\textup{#1}}% or \textnormal
% never use \text for anything but textual comments
\begin{document}
\begin{align*}
  Z &= \Tr\tsub{el,ph}\bigl[\exp(-\beta H)\bigr]\\
  &= \int\mathcal{D}q
  \Tr\tsub{el}\biggl[T_\tau\exp\biggl(-\int_0^\beta d\tau\sum_j\Bigl[
  \!
 \begin{aligned}[t]
   &-t\sum_\sigma\bigl(c_{j\sigma}^\dag(\tau)c_{j+1,\sigma}(\tau)+\text{h.c.}\bigr)\\
   &+\tfrac{M}{2}\bigl(\dot q_j(\tau)^2+\omega_0^2q_j(\tau)^2\bigr)\\
   &-g\sqrt{2M\omega_0}\sum_\sigma n_{j\sigma}(\tau)q_j(\tau)\Bigr]\biggr)\biggr]
 \end{aligned}\\
 &= ...
\end{align*}

The above waste a bit too much space IMO. Here is another

\begin{align*}
  Z &= \Tr\tsub{el,ph}\bigl[\exp(-\beta H)\bigr]\\
  &= \int\mathcal{D}q
  \Tr\tsub{el}
  \begin{aligned}[t]
  \biggl[&T_\tau\exp\biggl(-\int_0^\beta d\tau\sum_j
    \Bigl[
        -t\sum_\sigma\bigl(c_{j\sigma}^\dag(\tau)c_{j+1,\sigma}(\tau)+\text{h.c.}\bigr)
    \\
    &+\tfrac{M}{2}\bigl(\dot q_j(\tau)^2+\omega_0^2q_j(\tau)^2\bigr)
    \sqrt{2M\omega_0}\sum_\sigma
    n_{j\sigma}(\tau)q_j(\tau)\Bigr]\biggr)\biggr]
  \end{aligned}
  \\
  &= ...
\end{align*}
\end{document}