First up is the Feynman slash, i first tried hacking something up myself:
\renewcommand{\slash}{\hskip -3pt\not\hskip -2pt}
this however has a few issues because it would need to be skipped differently for different letters, the line width of the slash was never quite right and it's too low.
After some more googling i found the slashed package. Which looks better:
Next up was a contraction symbolized by an underbracket. This functionality is provided by the mathtools package except that it looked to big for the fonts i use. Fortunately there are some optional arguments that fix that issue.
\newcommand{\contraction}[1]{\underbracket[0.2ex][0.5ex]{#1}}
And now comes my favourite: My Quantum field theory professor decided to make up a nonstandard way of being undecided about whether we are in a continous or discrete space and just superimposed a sum and an integral instead of using common sense and Dirac measures.
Marvel at this beauty:
\newcommand{\Sunt}[1]{\hskip5pt\int\hskip -15pt \sum_{#1}\kern 2pt}
\newcommand{\sunt}{\hskip3pt\int\hskip -10pt \sum}
Of course capital is for Displaystyle.