How to type the small letter corresponding to $\mathscr{G}$?

Question

how to type ???

This is a math symbol in the renormalization group theory. The mathrsfs can only support capital letter.

Sorry everybody, I made a serious mistake! I thought the G in the picture is a lowercase letter. But in fact it is already a uppercase letter.

I'am very sorry.

Answer 1

Does this help?

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{calligra,amsmath,amssymb}

\newcommand{\g}{\text{\calligra g}\,}

\begin{document}

$\g\colon \mathbb{R}\to \mathcal{W}$

\end{document}

Answer 2

This should do it.

\documentclass[12pt]{article}
\usepackage{unicode-math}
\setmathfont{XITS Math}
\setmathfont[version=setB,StylisticSet=1]{XITS Math}
\begin{document}
$\delta \mathscr{G_i}$
\end{document} 

Now, first You have to define a math font, e.g. XITS Math and then the letter G will appear as required. You need to compile this with xelatex to get the output.

An alternative using the mathrsfs package. The MWE:

\documentclass[12pt]{article}
\usepackage{mathrsfs}
\begin{document}
$\delta~\mathscr{G}_i$
\end{document} 

You can use pdflatex itself to compile this. And to remove the gap, just remove the ~ symbol.

Answer 3

If a given font family provides only uppercase letters and no lowercase letters, it's generally going to be tricky to find a substitute font whose lowercase letters provide a stylistic match to the uppercase letters of the initial font.

You may want to give the Zapf Chancery script font a try. You'll notice immediately that its letters are both less slanted and less ornate than the uppercase letters of the mathrsfs script font. Of course, this may be to your liking. (Speaking strictly for myself, I find that the script-G provided by mathrsfs looks out of place next to the \delta character from the Computer Modern family.)

For sure, if you decide to use \mathpzc{g} in your document, you should also use the same font family for the uppercase-G, i.e., write \mathpzc{G}. Don't use \mathscr{G} next to \mathpzc{g} unless you want to set up a massive visual clash..

\documentclass{article}
\usepackage{mathrsfs}
\DeclareMathAlphabet{\mathpzc}{OT1}{pzc}{m}{it} % load "Zapf Chancery" as a math alphabet
\begin{document}
$\mathpzc{g}$ $\mathpzc{G}$ \quad $\delta\mathpzc{g}_i$ $\delta\mathpzc{G}_i$ 

\medskip
for comparison: $\delta\mathscr{G}_i$
\end{document}