How do I select the style of a lowercase gamma?

Question

It is traditional in Physics to use a lowercase gamma that looks like a Y. Without going into the question of whether that tradition is wrong, how do I differentiate in math mode Latex markup between a Gamma that looks like a Y and a Gamma with a loop?

No, I do not mean either capital or upright.

I'd prefer avoiding Unicode unless ArXiV now supports xetex.

I don't know how to insert the PDF as an image, but http://mason.gmu.edu/~smetz3/humor/dirac.pdf is generated from

\documentclass{article}
\usepackage{bm}
\usepackage[paperheight=10in,paperwidth=10in,top=0.75in, bottom=0in,   left=0in, right=0in]{geometry}
\usepackage{graphicx}
\begin{document}
\pagestyle{empty}

\vspace{.5in}

\begin{center}
{\Huge \bfseries Which part of}
\end{center}

\vspace{1.75in}

{\Huge
  \[
    \bm{(\gamma^{\mu } (i\hbar \partial _{\mu } - {\frac {e}{c}}A_{\mu })-mc) \psi =0}
  \]
}

\vspace{1.75in}

\begin{center}
{\Huge \bfseries don't you understand?}
\end{center}
\end{document}

Answer 1

Please choose one of these.

\documentclass[a4paper]{article}
\usepackage{tipa}
\usepackage{upgreek}
\begin{document}

\begin{tabular}{rl}
tipa:    & \textbabygamma\\
upgreek: & $\upgamma$\\
tipa:    & \textgamma\\
tipa:    & \textramshorns\\
default: & $\gamma$\\
\end{tabular}

\end{document}

Answer 2

In the Modern Toolchain

\usepackage{unicode-math}, then check the list of Unicode-math symbols for a font specimen of all the math symbols in a half-dozen Unicode math fonts. Pick a font you like.

If you want to change only the Greek letters to another Unicode font, including any of the fonts on your desktop, add \setmathfont{Latin Modern Math}, as your default, then \setmathfont[range=it/{Greek,greek}, Scale=MatchLowercase]{Artemisia} (for example).

In general, write your new documents for the new toolchain if you can, and the legacy toolchain if you have to.

With Legacy Math Fonts

Load isomath and pick one of the Greek alphabets it supports. This package and mathalfa give you the closest thing the NFSS ecosystem has to a standard interface for selecting the math alphabets of your choice.

With Legacy Greek Text Fonts

You can use LGR-encoded legacy NFSS fonts in math mode through mathastext. This example loads GFS Bodoni:

\usepackage[LGR,T1]{fontenc}
\usepackage{textcomp}
\usepackage[utf8]{inputenc}
%\usepackage{amsmath}
\usepackage{alphabeta}
\usepackage{gfsbodoni}
\usepackage[italic, LGRgreek, itgreek]{mathastext} % or upgreek, or upGreek.

If you want to write actual Greek words, also load babel.

If You Really Want Just that One Letter

Look up the encoding of the legacy font whose symbol you want, and declare it as a symbol alphabet. This example typesets the Euler-Mascheroni constant with the γ from the font AMS Euler, in ISO style. The constant is unslanted, not italic, and I give it the de facto standard name \upgamma. The other symbols are taken from newpx, a clone of Palatino, another font by Hermann Zapf that goes well with his AMS Euler.

\documentclass[varwidth]{standalone}
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\usepackage[utf8]{inputenc} % The default since 2018.
\usepackage{newpxtext, newpxmath}

\DeclareSymbolFont{eulerup}{U}{zeur}{m}{n}
\DeclareMathSymbol{\upgamma}{\mathord}{eulerup}{"0D}

\begin{document}
\begin{minipage}{10cm}
\[ \upgamma = \lim_{n \to \infty} \left(
      - \ln n + \sum_{k=1}^n \frac{1}{k}
   \right) \]
\end{minipage}
\end{document}

By the way, if you like this setup, here is how you get it with the modern toolchain (after downloading Khaled Hosny’s font Neo Euler from GitHub):

\documentclass[varwidth]{standalone}
\usepackage[math-style=ISO]{unicode-math}

\defaultfontfeatures{Scale=MatchLowercase}
\setmainfont{TeX Gyre Pagella}[
  Scale = 1.0 ,
  Ligatures = {Common, TeX} ]
\setmonofont{Inconsolata}
% A good matching sans serif, should you want one, is Optima.  A free clone
% is URW Classico.
\setmathfont{TeX Gyre Pagella Math}
% Neo Euler by Khaled Hosny, based on AMS Euler by Hermann Zapf:
% https://github.com/khaledhosny/euler-otf
\setmathfont[range=up/{latin,Latin,greek,Greek},
             script-style={},
             sscript-style={}]{Neo Euler}

\begin{document}
\begin{minipage}{10cm}
\[ \upgamma = \lim_{n \to \infty} \left(
      - \ln n + \sum_{k=1}^n \frac{1}{k}
   \right) \]
\end{minipage}
\end{document}