# A C*-algebraic approach to interacting quantum field theories

February 16, 2019

A novel C*-algebraic framework is presented for relativistic quantum field
theories, fixed by a Lagrangean. It combines the postulates of local quantum
physics, encoded in the Haag-Kastler axioms, with insights gained in the
perturbative approach to quantum field theory. Key ingredients are an
appropriate version of Bogolubov's relative $S$-operators and a reformulation
of the Schwinger-Dyson equations. These are used to define for any classical
relativistic Lagrangean of a scalar field a non-trivial local net of
C*-algebras, encoding the resulting interactions at the quantum level. The
construction works in any number of space-time dimensions. It reduces the
longstanding existence problem of interacting quantum field theories in
physical spacetimeto the question of whether the C*-algebras so constructed
admit suitable states, such as stable ground and equilibrium states. The method
is illustrated on the example of a non-interacting field and it is shown how to
pass from it within the algebra to interacting theories by relying on a
rigorous local version of the interaction picture.

open access link

@article{Buchholz:2019rem,
author = "Buchholz, Detlev and Fredenhagen, Klaus",
title = "{A C*-algebraic approach to interacting quantum field
theories}",
year = "2019",
eprint = "1902.06062",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1902.06062;%%"
}

Keywords:

*none*