\begin{thebibliography}{32}
\expandafter\ifx\csname natexlab\endcsname\relax\def\natexlab#1{#1}\fi
\expandafter\ifx\csname bibnamefont\endcsname\relax
  \def\bibnamefont#1{#1}\fi
\expandafter\ifx\csname bibfnamefont\endcsname\relax
  \def\bibfnamefont#1{#1}\fi
\expandafter\ifx\csname citenamefont\endcsname\relax
  \def\citenamefont#1{#1}\fi
\expandafter\ifx\csname url\endcsname\relax
  \def\url#1{\texttt{#1}}\fi
\expandafter\ifx\csname urlprefix\endcsname\relax\def\urlprefix{URL }\fi
\providecommand{\bibinfo}[2]{#2}
\providecommand{\eprint}[2][]{\url{#2}}

\bibitem[{\citenamefont{Feynman}(1948)}]{Feynman_1}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Feynman}},
  \bibinfo{journal}{Reviews of Modern Physics} \textbf{\bibinfo{volume}{2}},
  \bibinfo{pages}{367} (\bibinfo{year}{1948}).

\bibitem[{\citenamefont{Feynman and Hibbs}(1965)}]{Feynman_2}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Feynman}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.~R.} \bibnamefont{Hibbs}},
  \emph{\bibinfo{title}{Quantum Mechanics and Path Integrals}}
  (\bibinfo{publisher}{McGraw-Hill, USA}, \bibinfo{year}{1965}).

\bibitem[{\citenamefont{Muldowney}(2012)}]{Muldowney}
\bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Muldowney}},
  \emph{\bibinfo{title}{A Modern Theory of Random Variation}}
  (\bibinfo{publisher}{Wiley, N.J.}, \bibinfo{year}{2012}).

\bibitem[{\citenamefont{Nathanson and J{\o}rgensen}(2015)}]{Katya_1}
\bibinfo{author}{\bibfnamefont{E.~S.} \bibnamefont{Nathanson}}
  \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{E.}~\bibnamefont{J{\o}rgensen},
  \bibfnamefont{Palle}}, \bibinfo{journal}{J. Math. Phys.}
  \textbf{\bibinfo{volume}{56}}, \bibinfo{pages}{092102}
  (\bibinfo{year}{2015}).

\bibitem[{\citenamefont{Nathanson}(2015)}]{Katya_2}
\bibinfo{author}{\bibfnamefont{E.~S.} \bibnamefont{Nathanson}},
  \bibinfo{journal}{University of Iowa Thesis}  (\bibinfo{year}{2015}).

\bibitem[{\citenamefont{Richtmyer et~al.}(1947)\citenamefont{Richtmyer, Pasta,
  and Ulam}}]{Ulam}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Richtmyer}},
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Pasta}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{S.}~\bibnamefont{Ulam}},
  \bibinfo{journal}{LANL report} \textbf{\bibinfo{volume}{LAMS 551}}
  (\bibinfo{year}{1947}).

\bibitem[{\citenamefont{Metropolis and S.}(1949)}]{Metropolis}
\bibinfo{author}{\bibfnamefont{N.}~\bibnamefont{Metropolis}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{U.}~\bibnamefont{S.}},
  \bibinfo{journal}{Journal of the American Statistical Association}
  \textbf{\bibinfo{volume}{44}}, \bibinfo{pages}{335} (\bibinfo{year}{1949}).

\bibitem[{\citenamefont{Luscher and Wolff}(1990)}]{Luscher}
\bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Luscher}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{U.}~\bibnamefont{Wolff}},
  \bibinfo{journal}{Nuclear Physics} \textbf{\bibinfo{volume}{B339}},
  \bibinfo{pages}{222} (\bibinfo{year}{1990}).

\bibitem[{\citenamefont{Luscher}(1986)}]{Luscher2}
\bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Luscher}},
  \bibinfo{journal}{Comm. Math. Phys.} \textbf{\bibinfo{volume}{105}},
  \bibinfo{pages}{153} (\bibinfo{year}{1986}).

\bibitem[{\citenamefont{Bing-Nan et~al.}(2016)\citenamefont{Bing-Nan, A., Lee,
  and Mei{\ss}ner}}]{Lee}
\bibinfo{author}{\bibfnamefont{L.}~\bibnamefont{Bing-Nan}},
  \bibinfo{author}{\bibfnamefont{L.~T.} \bibnamefont{A.}},
  \bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Lee}}, \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{U.~G.} \bibnamefont{Mei{\ss}ner}},
  \bibinfo{journal}{Phys. Letters B} \textbf{\bibinfo{volume}{760}},
  \bibinfo{pages}{309} (\bibinfo{year}{2016}).

\bibitem[{\citenamefont{Luu and Savage}(2011)}]{Luu}
\bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Luu}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{M.~J.} \bibnamefont{Savage}},
  \bibinfo{journal}{Phys. Rev. D.} \textbf{\bibinfo{volume}{83}},
  \bibinfo{pages}{114508} (\bibinfo{year}{2011}).

\bibitem[{\citenamefont{Aiello and Polyzou}(2016)}]{Gordon}
\bibinfo{author}{\bibfnamefont{G.~J.} \bibnamefont{Aiello}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{W.~N.} \bibnamefont{Polyzou}},
  \bibinfo{journal}{Phys. Rev. D} \textbf{\bibinfo{volume}{93}},
  \bibinfo{pages}{056003} (\bibinfo{year}{2016}).

\bibitem[{\citenamefont{Faddeev and Slavnov}(1980)}]{Faddeev}
\bibinfo{author}{\bibfnamefont{L.~D.} \bibnamefont{Faddeev}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{A.~A.} \bibnamefont{Slavnov}},
  \emph{\bibinfo{title}{Gauge Fields, Introduction to Quantum Theory}},
  vol.~\bibinfo{volume}{I} (\bibinfo{publisher}{Benjamin Cummings, Reading,
  Mass.}, \bibinfo{year}{1980}).

\bibitem[{\citenamefont{Rosenfelder}(2009)}]{Rosenfelder1}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Rosenfelder}},
  \bibinfo{journal}{Phys. Rev. A} \textbf{\bibinfo{volume}{79}},
  \bibinfo{pages}{012701} (\bibinfo{year}{2009}).

\bibitem[{\citenamefont{Carron and Rosenfelder}(2011)}]{Rosenfelder2}
\bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Carron}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Rosenfelder}},
  \bibinfo{journal}{Phys. Letters. A} \textbf{\bibinfo{volume}{375}},
  \bibinfo{pages}{3781} (\bibinfo{year}{2011}).

\bibitem[{\citenamefont{Campbell et~al.}(1975)\citenamefont{Campbell, Finkler,
  C.~E.~Jones, and Misheloff}}]{Campbell}
\bibinfo{author}{\bibfnamefont{W.~B.} \bibnamefont{Campbell}},
  \bibinfo{author}{\bibfnamefont{P.}~\bibnamefont{Finkler}},
  \bibinfo{author}{\bibfnamefont{C.~E.} \bibnamefont{C.~E.~Jones}},
  \bibnamefont{and} \bibinfo{author}{\bibfnamefont{M.~N.}
  \bibnamefont{Misheloff}}, \bibinfo{journal}{Phys. Rev. D}
  \textbf{\bibinfo{volume}{12}}, \bibinfo{pages}{2363} (\bibinfo{year}{1975}).

\bibitem[{\citenamefont{Henstock}(1963)}]{Henstock}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Henstock}},
  \emph{\bibinfo{title}{Theory of Integration}}
  (\bibinfo{publisher}{Butterworths, London}, \bibinfo{year}{1963}).

\bibitem[{\citenamefont{Bartle}(2001)}]{bartle}
\bibinfo{author}{\bibfnamefont{R.~G.} \bibnamefont{Bartle}},
  \emph{\bibinfo{title}{A modern theory of integration}},
  vol.~\bibinfo{volume}{32} (\bibinfo{publisher}{American Mathematical Society,
  Providence, RI}, \bibinfo{year}{2001}).

\bibitem[{\citenamefont{Gill and Zachary}(2008)}]{Gill}
\bibinfo{author}{\bibfnamefont{T.}~\bibnamefont{Gill}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{W.}~\bibnamefont{Zachary}},
  \bibinfo{journal}{Real Analysis Exchange} \textbf{\bibinfo{volume}{34}},
  \bibinfo{pages}{1} (\bibinfo{year}{2008}).

\bibitem[{\citenamefont{Reed and Simon}(1980)}]{Simon}
\bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Reed}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{B.}~\bibnamefont{Simon}},
  \emph{\bibinfo{title}{Methods of Modern Mathematical Physics}},
  vol.~\bibinfo{volume}{I} (\bibinfo{publisher}{Academic Press, San Diego},
  \bibinfo{year}{1980}).

\bibitem[{\citenamefont{Nathanson and J{\o}rgensen}(2017)}]{Katya_3}
\bibinfo{author}{\bibfnamefont{E.~S.} \bibnamefont{Nathanson}}
  \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{E.}~\bibnamefont{J{\o}rgensen},
  \bibfnamefont{Palle}}, \bibinfo{journal}{J. Math. Phys.}
  \textbf{\bibinfo{volume}{58}}, \bibinfo{pages}{122101}
  (\bibinfo{year}{2017}).

\bibitem[{\citenamefont{Dollard}(1964)}]{Dollard}
\bibinfo{author}{\bibfnamefont{J.~D.} \bibnamefont{Dollard}},
  \bibinfo{journal}{J. Math. Phys.} \textbf{\bibinfo{volume}{5}},
  \bibinfo{pages}{729} (\bibinfo{year}{1964}).

\bibitem[{\citenamefont{Dollard and Friedman}(1978)}]{dollard:1978we}
\bibinfo{author}{\bibfnamefont{J.~D.} \bibnamefont{Dollard}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{C.~N.} \bibnamefont{Friedman}},
  \bibinfo{journal}{Annals Phys.} \textbf{\bibinfo{volume}{111}},
  \bibinfo{pages}{251} (\bibinfo{year}{1978}).

\bibitem[{\citenamefont{Haag}(1958)}]{Haag:1958vt}
\bibinfo{author}{\bibfnamefont{R.}~\bibnamefont{Haag}}, \bibinfo{journal}{Phys.
  Rev.} \textbf{\bibinfo{volume}{112}}, \bibinfo{pages}{669}
  (\bibinfo{year}{1958}).

\bibitem[{\citenamefont{Ruelle}(1962)}]{Ruelle:1962}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Ruelle}},
  \bibinfo{journal}{Helv. Phys. Acta.} \textbf{\bibinfo{volume}{35}},
  \bibinfo{pages}{147} (\bibinfo{year}{1962}).

\bibitem[{\citenamefont{Lippmann and Schwinger}(1950)}]{Lippmann}
\bibinfo{author}{\bibfnamefont{B.~A.} \bibnamefont{Lippmann}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{J.}~\bibnamefont{Schwinger}},
  \bibinfo{journal}{Physical Review} \textbf{\bibinfo{volume}{79}},
  \bibinfo{pages}{409 eq 1.63} (\bibinfo{year}{1950}).

\bibitem[{\citenamefont{Nelson}(1964)}]{Nelson}
\bibinfo{author}{\bibfnamefont{E.}~\bibnamefont{Nelson}},
  \bibinfo{journal}{Journal of Mathematical Physics}
  \textbf{\bibinfo{volume}{5}}, \bibinfo{pages}{332} (\bibinfo{year}{1964}).

\bibitem[{\citenamefont{Abramowitz and Stegun}(1964)}]{Abramowitz}
\bibinfo{author}{\bibfnamefont{M.}~\bibnamefont{Abramowitz}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{I.}~\bibnamefont{Stegun}},
  \emph{\bibinfo{title}{Handbook of Mathematical Functions}},
  vol.~\bibinfo{volume}{55} (\bibinfo{publisher}{National Bureau of Standards,
  Washington DC.}, \bibinfo{year}{1964}).

\bibitem[{\citenamefont{M{\o}ller}(1945)}]{Moller}
\bibinfo{author}{\bibfnamefont{C.}~\bibnamefont{M{\o}ller}},
  \bibinfo{journal}{Det. Kggl. Danske Videnskaberbernes Selskab,
  Matematisk-Fysiske Meddelelser} \textbf{\bibinfo{volume}{23(1)}}
  (\bibinfo{year}{1945}).

\bibitem[{\citenamefont{Mulherin and Zinnes}(1970)}]{Mulherin}
\bibinfo{author}{\bibfnamefont{D.}~\bibnamefont{Mulherin}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{I.~I.} \bibnamefont{Zinnes}},
  \bibinfo{journal}{J. Math. Phys.} \textbf{\bibinfo{volume}{11}},
  \bibinfo{pages}{1402} (\bibinfo{year}{1970}).

\bibitem[{\citenamefont{Busalev and Matveev}(1970)}]{Busalev}
\bibinfo{author}{\bibfnamefont{V.~S.} \bibnamefont{Busalev}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{V.~B.} \bibnamefont{Matveev}},
  \bibinfo{journal}{Theoret. and Math. Phys.} \textbf{\bibinfo{volume}{2}},
  \bibinfo{pages}{266} (\bibinfo{year}{1970}).

\bibitem[{\citenamefont{Kr\"oger and Slobodrian}(1984)}]{kroger}
\bibinfo{author}{\bibfnamefont{H.}~\bibnamefont{Kr\"oger}} \bibnamefont{and}
  \bibinfo{author}{\bibfnamefont{R.~J.} \bibnamefont{Slobodrian}},
  \bibinfo{journal}{Phys. Rev. C.} \textbf{\bibinfo{volume}{30}},
  \bibinfo{pages}{1390} (\bibinfo{year}{1984}).

\end{thebibliography}
