Mirror greek symbol in math environment

Question

I need a mirrored symbol \Gamma. Is it posible? I can't find this symbol and I do not know a way to mirror the symbol. I use unicode math.

Answer 1

You can use \reflectbox from graphicx and also \text from amsmath to get the symbol to scale in sub/superscripts

\documentclass{article}
\usepackage{amsmath,graphicx}
\usepackage{unicode-math}
\setmathfont{Lucida Bright Math OT}

\DeclareRobustCommand{\ammaG}{\text{\reflectbox{$\Gamma$}}}

\begin{document}

$\Gamma\ne\ammaG$

$\Gamma=\Gamma$

$\ammaG_{\ammaG_\ammaG}$

\end{document}

It's better to use \DeclareRobustCommand so there's no problem using the new symbol in moving arguments. Of course you can't copy-paste it as a reversed Gamma, but the symbol is not in Unicode anyway.

If one needs an “almost reflected” version of \varGamma, some pain is needed for kerning subscripts:

\documentclass{article}
\usepackage{amsmath,graphicx}
\usepackage{xparse}

\NewDocumentCommand{\antivarGamma}{e{_^}}{%
  {\mathpalette\makeantigamma\relax}%
  \IfValueT{#1}{_{\kernforantigamma{#1}}}%
  \IfValueT{#2}{^{#2}}%
}

\makeatletter
\newcommand{\makeantigamma}[2]{%
  \reflectbox{\raisebox{\depth}{\scalebox{1}[-1]{$\m@th#1 L$}}}%
}
\newcommand{\kernforantigamma}[1]{\mathpalette\kern@for@antigamma{#1}}
\newcommand{\kern@for@antigamma}[2]{%
  \begingroup
  \sbox\z@{$\m@th\promote@style#1{\kern0ptI}_{#2}$}%
  \sbox\tw@{$\m@th\promote@style#1I_{#2}$}%
  \kern\dimexpr\wd\tw@-\wd\z@ #2
  \endgroup
}
\newcommand{\promote@style}[1]{%
  \ifx#1\scriptstyle\textstyle\else\scriptstyle\fi
}
\makeatother

\begin{document}

$
-I_{kl}\antivarGamma_{m}=g_{km}\antivarGamma{l}-g_{lm}\antivarGamma_{k}
\qquad
\varGamma_{k}^{*}=\antivarGamma{k}^{\dagger}\varLambda
$
\end{document}

The \antivarGamma symbol appears in a 1945 paper on the Dirac equation (Proceedings of the Royal Society). See Is there a TeX symbol that looks like this reverse uppercase gamma?

Source: H. Chandra, “The correspondence between the particle and the wave aspects of the meson and the photon,” Proc. R. Soc. London, Ser. A 186(1007), 502–525 (1946).