align env - some symbols are non-italic?

Question

I am confused about the behavior of my ams align evironment. Minimalistic example:

\documentclass[english]{article}
\usepackage{amsmath}

\begin{document}


\begin{align*}
\rm{d}x_{\tau} &= R(u) v \rm{d} \tau, \\
\rm{d}v_{\tau} &= - R(u)\nabla U(x)\rm{d}\tau -\gamma v R(u) \rm{d}\tau + \sqrt{\frac{2\gamma R(u)}{\beta}}\rm{d}W_{\tau}
\end{align*}


\end{document}

Output:

Why are some symbols like "x" or "u" parsed differently, sometimes italic and sometimes not?

Answer 1

The commands \rm, \it, \bf and similar two-letter font changing commands have been deprecated for almost 30 years. Moreover, they didn't take arguments, being declarations. The correct syntax 30 years ago (or more) would have been {\rm d}. Never use them.

Make yourself a favor and use a different strategy, namely

\newcommand{\diff}{\mathop{}\!\mathrm{d}}

so you get several advantages, among which

• the spacing is good in (almost) every situation, automatically;
• you can change to an italic “d” whenever you want, just by replacing \mathrm{d} with d.

\documentclass{article}
\usepackage{amsmath}

\newcommand{\diff}{\mathop{}\!\mathrm{d}}

\begin{document}

\begin{align*}
\diff x_{\tau} &= R(u) v \diff\tau, \\
\diff v_{\tau} &= - R(u)\nabla U(x)\diff\tau -\gamma v R(u) \diff\tau
  + \sqrt{\frac{2\gamma R(u)}{\beta}}\diff W_{\tau}
\end{align*}

\end{document}

Answer 2

You can use the fixdif package, which redefines \d macro in math mode.

\documentclass{article}
\usepackage{fixdif}
\usepackage{amsmath}
\begin{document}

\begin{align*}
  \d x_{\tau} &= R(u) v \d\tau, \\
  \d v_{\tau} &= - R(u)\nabla U(x)\d\tau -\gamma v R(u) \d\tau
    + \sqrt{\frac{2\gamma R(u)}{\beta}}\d W_{\tau}
\end{align*}

\end{document}

If you prefer the italic d for the differential operator, just use the normal option provided by the package.