mathmode spacing shorter than \quad?

A \quad corresponds to a length of 1em. In math mode, 1em=18mu. Use \mkern<n>mu, where <n> can be either a positive or a negative number, to exert very fine control over spacing. Note: no curly braces around <n>mu.

To space ahead by half a quad while in math mode, simply write \mkern9mu.

Two macros that provide standard abbreviations for math-mode spacing directives are

\, -- \mkern3mu  ("thinspace")
\! -- \mkern-3mu ("negative thinspace")

Is there a meaningful difference between a\hspace{0.5em}b and a\mkern9mu b? It usually will not make a difference for display-math material. However, it could make a difference for inline-math material. This is because TeX never discards explicit kerns (and \mkern is a kern); in contrast, \hspace could get discarded at the start and end of lines. Thus, if your document happens to have a longish inline math equation that's allowed to break across lines, using \mkern or \hspace inside the formula could make a difference. (If you wanted to allow potential line breaks while using mu-based spacing directives, don't use \mkern; instead, use \mskip instead.)

Citing the comment from @egreg:

" A quad is 1em; just use \hspace{0.5em} or \hspace{0.25em}. Indeed \quad means the same as \hspace{1em}. – egreg "

Thanks!

Therefore, might or not be helpful for some (for me it is convenient):

 \newcommand{\Hquad}{\hspace{0.5em}}