Typesetting multiletter variables with subscripts and mixed formatting

Question

Through my research on this website I've found the best way to typeset multiletter variables is using \mathit. However, if the variable has mixed formatting (i.e. bold, italic and roman) or super/subscript the results are not satisfactory with regards to spacing.

For my case, I'm trying to denote perturbations (denoted $\delta$) to variables $f_0$ and $\bm{f}_1$. Simply prepending the delta creates too much space, while putting the entire group in \mathit affects the subscript spacing and the bold font. I have attached my best attempts as a MWE below.

It would be helpful if there was a command called \mathgroup or something that would denote a multiletter variable without affecting formatting.

\documentclass[preview]{standalone}
\usepackage{amsmath}
\usepackage{bm}
\begin{document}
% Case 1
$ \mathit{\delta f_\mathrm{0}}$ has less subscript spacing between $f$ and 0 than \\
$\delta f_0$ and even less than than \\
$ \mathit{\delta f}_0$

% Case 2: The only way I've found to achieve something close to what I want except for spacing
$\mathit{\delta \bm{{f_{\mbox{\unboldmath$\scriptstyle 1$}}}}} $ appears identical to \\
$ \delta \bm{f}_1$ the following are not solutions either\\
$ \mathit{\delta \bm{{f}}_\mathrm{1}}$ \\
$ \mathit{\delta \bm{{f}}}_1$
\end{document}

Answer 1

You seem to want to kern the \delta with the next letter, pushing back an ‘f’ more than other letters.

I wouldn't do it, actually, but here's a proof of concept.

\documentclass{article}
\usepackage{amsmath,bm}

\makeatletter
\DeclareRobustCommand{\prt}{\mathop{}\!\delta\check@f}
\newcommand{\check@f}{%
  \@ifnextchar f{\mspace{-3mu}}{\check@bmf}%
}
\newcommand{\check@bmf}{%
  \@ifnextchar\bm{\check@bmf@i}{\mspace{-1.5mu}}%
}
\newcommand{\check@bmf@i}[2]{% #1 is \bm, #2 is the letter
  \if f\unexpanded{#2}%
    \mspace{-3mu}%
  \else
    \mspace{-1.5mu}%
  \fi
  \bm{#2}%
}
\makeatother

\begin{document}

$\prt g \prt f \prt\bm{f} \prt\bm{g}$

\end{document}

Answer 2

\documentclass{article}
\usepackage{amsmath}
\usepackage{bm}
\begin{document}

$ \delta f_0$ $ \delta \bm{f}_1$


$ \delta\!f_0$ $ \delta\!\bm{f}_1$


$ \delta \mkern-2mu f_0$ $ \delta \mkern-2mu \bm{f}_1$

\end{document}

\mathit is not appropriate here as there are no adjacent (latin) letters that need to be typeset as a word. i would probably use the first line, but if you want tighter spacing you can add a negative kern, I find the standard \! (-3mu by default) too much, but perhaps -2mu is an improvement.