Annotated equations

Question

I need many of my equations to have annotations stating their domain of validity, or certain conditions for which the equation is true. Preferably, these would be flush right against the equation number, and would otherwise not affect the alignment of the equation content. I would like to be able to write something like

\begin{equation}
  \sigma_{(j)}\, i = i\, \sigma_{(j)}
  \Domain{C_{1,3}}
\end{equation}

and have it set $C_{1,3}$ just before the equation number (maybe separated by a quad, say). I'm thinking maybe \Domain could temporarily redefine the \tag command (or whatever actually places the number on the line) in this equation, but I can't figure out how to do it. In particular, some equations won't have a \Domain command, and shouldn't set anything next to the equation number.

I found a very similar question in this forum, which suggested something that looks right in the equation itself:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
  \label{commutation}
  \sigma_{(j)}\, i = i\, \sigma_{(j)}
  \stepcounter{equation}
  \tag*{$C_{1,3}\quad$(\theequation)}
\end{equation}
References come out wrong, as when Eq.~\ref{commutation} is
referenced.
\end{document}

As the example points out, however, the reference to the equation number in the text comes out as $C_{1,3}\quad$(\theequation), rather than just (\theequation).

The amsmath documentation itself suggests using an align environment for this sort of thing, but that's unacceptable. (Also, if it makes any difference, I'm actually using revtex4-1, rather than article.)

Answer 1

This will over-print the equation if the equation gets too big.

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\def\maketag@@@#1{\@Domain\hbox{\m@th\normalfont#1}}
\def\Domain#1{\def\@Domain{\llap{$#1$\quad}}}
\Domain{}
\makeatother

\begin{document}
\begin{equation}
  \label{commutation}
  \sigma_{(j)}\, i = i\, \sigma_{(j)}
  \Domain{C_{1,3}}
\end{equation}
References come out wrong, as when Eq.~\ref{commutation} is
referenced.
\end{document}