How to rescale equations formatted using 'align'? Resizebox doesn't appear to work
It seems that scalebox doesn't work well with math mode. A possible solution is to put your align inside a minipage:
\documentclass[10pt, oneside, twocolumn, notitlepage]{book}
\usepackage{amsthm,latexsym,amssymb,amsmath, amsfonts}
\usepackage{graphicx}
\usepackage{lipsum}
\newtheorem{thm}{Theorem}[section]
\newtheorem{rem}[thm]{Remark}
\begin{document}
\lipsum[1]
\resizebox{.9\linewidth}{!}{
\begin{minipage}{\linewidth}
\begin{align*}
\mathrm{Term_{2a}} &=\iint \left[\nabla \phi_t(x) \cdot \nabla \phi(y) + \nabla \phi(x) \cdot \nabla \phi_t(y) \right]\ e^{-\frac{\|x-y\|^2}{d^2}} W_{l}(\phi(x))W_{l}(\phi(y)) \mathrm{\ dx \ dy} \\
&=\iint \nabla \phi_t(x) \cdot \nabla \phi(y) e^{-\frac{\|x-y\|^2}{d^2}} W_{l}(\phi(x))W_{l}(\phi(y)) \mathrm{\ dx \ dy} \\
\end{align*}
\end{minipage}
}
\lipsum
\end{document}