documentclass{article}
 usepackage[force]{feynmp-auto} %<-added force
 begin{document}
 begin{align}
 begin{fmffile}{simple_labels}
 begin{fmfgraph*}(40,25)
 fmfleft{i1,i2}
 fmfright{o1,o2}
 fmflabel{$e^-$}{i1}
 fmflabel{$e^+$}{i2}
 fmflabel{$e^+,mu^+$}{o1}
 fmflabel{$e^-,mu^-$}{o2}
 fmflabel{$isqrt{alpha}$}{v1}
 fmflabel{$isqrt{alpha}$}{v2}
 fmf{fermion}{i1,v1,i2}
 fmf{fermion}{o1,v2,o2}
 fmf{photon,label=$gamma,,Z^0$}{v1,v2}
 end{fmfgraph*}
 end{fmffile}
 &=text{foobar}notag\
 foo&=bar
 end{align}
 end{document}

(./mpFockLOE.tex [MP to PDF] (./mpFockLOE.1)This is MetaPost, version 2.000 (TeX Live 2017) (kpathsea version 6.2.3)
(/usr/local/texlive/2017/texmf-dist/metapost/base/mpost.mp
(/usr/local/texlive/2017/texmf-dist/metapost/base/plain.mp
Preloading the plain mem file, version 1.005) ) (./mpFockLOE.mp)
*

documentclass{article}
 usepackage[force]{feynmp-auto} %<-added force
 begin{document}
 [
 begin{aligned}
 begin{fmffile}{simple_labels}
 begin{fmfgraph*}(40,25)
 fmfleft{i1,i2}
 fmfright{o1,o2}
 fmflabel{$e^-$}{i1}
 fmflabel{$e^+$}{i2}
 fmflabel{$e^+,mu^+$}{o1}
 fmflabel{$e^-,mu^-$}{o2}
 fmflabel{$isqrt{alpha}$}{v1}
 fmflabel{$isqrt{alpha}$}{v2}
 fmf{fermion}{i1,v1,i2}
 fmf{fermion}{o1,v2,o2}
 fmf{photon,label=$gamma,,Z^0$}{v1,v2}
 end{fmfgraph*}
 end{fmffile}
 &=text{foobar}\
 foo&=bar
 end{aligned}
 ]
 end{document}