I realise that this is somewhat of a special question, but is it possible to have regular characters in formulas, where the left half is colored e.g. in red and the right half is colored in blue, similar to the image below?

I realise that this is somewhat of a special question, but is it possible to have regular characters in formulas, where the left half is colored e.g. in red and the right half is colored in blue, similar to the image below?

I'm not sure what this would be used for, but the only method I see is to typeset two copies of the same glyph, clipped and differently colored.
\documentclass{article}
\usepackage{trimclip,xcolor}
\newcommand{\Atwo}{%
\mbox{%
\def\Ahalf##1{\dimexpr.5\width ##1 0.025em\relax}
\textcolor{red}{\clipbox{0 0 {\Ahalf+} 0}{A}}%
\textcolor{blue}{\clipbox{{\Ahalf-} 0 0 0}{A}}%
}%
}
\begin{document}
\Atwo
\end{document}

The little correction depends on the character: the vertex of the A doesn't lie at the exact half.
The risk of optical effects is very big: here the horizontal stem doesn't seem to connect properly, but just because of the choice of the colors.
Why not with tikz (I know for sure... it is heavy).
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\newcommand{\Atwo}[3][A]{%
\begin{tikzpicture}
\begin{scope}
\node[inner sep=0pt,outer sep=0pt] (a) {\phantom{#1}};
\clip (a.south west) rectangle ($(a.north)-(0.5\pgflinewidth,0)$);
\node[inner sep=0pt,outer sep=0pt,text=#2] {#1};
\end{scope}
\clip (a.south east) rectangle ($(a.north)-(0.5\pgflinewidth,0)$);
\node[inner sep=0pt,outer sep=0pt,text=#3] {#1};
\end{tikzpicture}
}
\begin{document}
\Atwo{blue}{red} \Atwo[B]{green}{magenta}
\end{document}
