Scalar models of formally interacting non-standard quantum fields in Minkowski space-time
Abstract
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space-time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework of non-standard theories like hyperfunction or ultra-hyperfunction quantum field theory. Model theories of formally self-coupled interacting neutral scalar fields are solved and discussed from a non-perturbative point of view.
References
\bibitem{PCT}
R.~F.~Streater, A.~S.~Wightman,
\emph{\it PCT, Spin, Statistics and All That},
Benjamin-Cummings Publishing Company, 1964.
\bibitem{Constantinescu}
F.~Constantinescu,
\emph{Distributionen und ihre Anwendungen in der Physik},
B. G. Teubner, 1974.
\bibitem{NagaMugi}
N.~Mugibayashi, S.~Nagamachi,
\emph{Hyperfunction quantum field theory},
Commun. Math. Phys. {\bf{46}} (1976) 119-134
[https://doi.org/10.1007/BF01608492].
\bibitem{NagBru}
S.~Nagamachi, E.~Br\"uning,
{\emph{Hyperfuction quantum field theory: Analytic structure, modular aspects,
and local observable algebras}},
J. Math. Phys. {\bf{42}} (2001) 99-129
[https://doi.org/10.1063/1.1326460].
\bibitem{Vindas}
A.~Debrouwere, J.~Vindas,
{\emph{On the non-triviality of certain spaces of analytic functions. Hyperfunctions and
ultrahyperfunctions of fast growth}},
Rev. R. Acad. Cienc. Exactas F\'is. Nat. Ser. A. Math. RACSAM 112 (2018) 473-508
[arXiv:1608.07859 [math.FA]].
\bibitem{FreundNambu}
P.~Freund, Y.~Nambu,
{\emph{Scalar Fields Coupled to the Trace of the Energy-Momentum Tensor}},
Phys. Rev. {\bf{174}} (1968) 1741-1743
[https://doi.org/10.1103/PhysRev.174.1741].
\bibitem{DeserHalpern}
S.~Deser, L.~Halpern,
{\emph{Self-coupled Scalar Gravitation}},
Gen. Rel. Grav. {\bf{1}}, No.2 (1970) 131-136
[https://doi.org/10.1007/BF00756892].
\bibitem{Nordstroem}
G.~Nordstr\"om,
{\emph{Zur Theorie der Gravitation vom Standpunkt des Re\-la\-tivi\-t\"ats\-prin\-zips}},
Ann. d. Physik {\bf{42}} (1913) 533-554
[https://doi.org/10.1002/andp.19133471303].
\end{thebibliography}
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