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Hi I need the syntax for a wick contraction under a number that goes to infinity. Essentially the sum going over all contractions. The right side of the contraction doesn't have an end essentially. Does anyone know how to do that? The last equation on the photo is what I need to be able to write.

simpler-wick it is arguably easier to hack.

documentclassarticle
usepackagesimpler-wick
newififWickCut
WickCutfalse
pgfkeys
 /simplerwick/.cd,
 cut/.code=WickCuttrue,
 no cut/.code=WickCutfalse,
 cut ratio/.initial=0.5


makeatletter
defswick@end#1#2
 swick@setfalse@#1
 tikzexternaldisable
 begintikzpicture[remember picture, baseline=(swick-close#1.base)]
 node[use as bounding box, inner sep=0pt, outer sep=0pt] (swick-close#1) $displaystyle #2$;
 endtikzpicture
 tikz[remember picture, overlay]
ifWickCut 
 draw ($(swick-open#1.south) + (0, -1pt)$) 
 -- ($(swick-open#1.base) + (0,3pt -1*swick@offset) + #1*(0, -1*swick@sep)$) 
 -- ($($(swick-open#1.base)!pgfkeysvalueof/simplerwick/cut ratio!(swick-close#1.base)$) + (0,3pt -1*swick@offset) + #1*(0, -1*swick@sep)$) 
else 
 draw ($(swick-open#1.south) + (0, -1pt)$) 
 -- ($(swick-open#1.base) + (0,3pt -1*swick@offset) + #1*(0, -1*swick@sep)$) 
 -- ($(swick-close#1.base) + (0,3pt -1*swick@offset) + #1*(0, -1*swick@sep)$) 
 -- ($(swick-close#1.south) + (0,-1pt)$);
fi
 tikzexternalenable
makeatother
begindocument
beginequation
 wickc1 phi c2 psi A c2 psi c1 phi
endequation
beginequation
 wick[cut]c1 phi c2 psi A c2 psi c1 phi
endequation
beginequation
 wick[cut,cut ratio=0.7]c1 phi c2 psi A c2 psi c1 phi
endequation
enddocument

The simplewick package is indeed quite simple, so it's not difficult to produce new commands from its code to do what you want. Here are open on the right contractions arcontraction and brcontraction. If you also need open on the left contractions, then you can do analogous commands commenting out the left vertical bar. The syntax of simplewick is somewhat cumbersome, so I would be more inclined to adapt the method described here if I were to implement this functionality myself.

documentclassarticle

usepackagesimplewick
makeatletter
newcommandbrcontraction[5][1ex]%
 mathchoice
 brcontraction@displaystyle#2#3#4#5#1%
 brcontraction@textstyle#2#3#4#5#1%
 brcontraction@scriptstyle#2#3#4#5#1%
 brcontraction@scriptscriptstyle#2#3#4#5#1
newcommandbrcontraction@[6]%
 setboxswb@xone=hbox$#1#2$%
 setboxswb@xtwo=hbox$#1#3$%
 setboxswb@xthree=hbox$#1#4$%
 setboxswb@xfour=hbox$#1#5$%
 swdimen@ne=wdswb@xtwo%
 advanceswdimen@ne by wdswb@xfour%
 divideswdimen@ne by 2%
 advanceswdimen@ne by wdswb@xthree%
 lower 0.5ex vbox%
 hbox to 0pt%
 kern wdswb@xone%
 kern 0.5wdswb@xtwo%
 brcontraction@@swdimen@ne#6%
 hss%
 
newcommandbrcontraction@@[3][0.05em]%
 hbox%
 swdimentw@=#3
 advanceswdimentw@ by -#1
 vrule width #1 height 0pt depth #3%
 lowerswdimentw@hboxvrule width #2 height 0pt depth #1%
% vrule width #1 height 0pt depth #3% commented out from original code
 relax
newcommandbrcontracted[5][1ex]%
 brcontraction[#1]#2#3#4#5ensuremath#2#3#4#5
newcommandarcontraction[5][1ex]%
 mathchoice
 arcontraction@displaystyle#2#3#4#5#1%
 arcontraction@textstyle#2#3#4#5#1%
 arcontraction@scriptstyle#2#3#4#5#1%
 arcontraction@scriptscriptstyle#2#3#4#5#1%
newcommandarcontraction@[6]%
 setboxswb@xone=hbox$#1#2$%
 setboxswb@xtwo=hbox$#1#3$%
 setboxswb@xthree=hbox$#1#4$%
 setboxswb@xfour=hbox$#1#5$%
 swdimen@ne=wdswb@xtwo%
 advanceswdimen@ne by wdswb@xfour%
 divideswdimen@ne by 2%
 advanceswdimen@ne by wdswb@xthree%
 vbox%
 hbox to 0pt%
 kern wdswb@xone%
 kern 0.5wdswb@xtwo%
 arcontraction@@swdimen@ne#6%
 hss%
 vskip 0.5ex% how far above the line starts
 vskiphtswb@xtwo
newcommandarcontraction@@[3][0.05em]%
 hbox%
 vrule width #1 height 0pt depth #3%
 vrule width #2 height 0pt depth #1%
% vrule width #1 height 0pt depth #3% commented out from original code
 relax
newcommandarcontracted[5][1ex]%
 arcontraction[#1]#2#3#4#5ensuremath#2#3#4#5
begindocument

[
arcontraction[2ex]ABC
arcontractionABCD
ABCDdots
]
[
brcontraction[2ex]ABC
brcontractionABCD
ABCDdots
]

[
brcontraction[2ex]sum n[ABCD
brcontractionsum n[ABCD
sum n[hatAhatBhatChatDdots]
]

enddocument