# Covariant homogeneous nets of standard subspaces

October 14, 2020

Rindler wedges are fundamental localization regions in AQFT. They are
determined by the one-parameter group of boost symmetries fixing the wedge. The
algebraic canonical construction of the free field provided by
Brunetti-Guido-Longo (BGL) arises from the wedge-boost identification, the BW
property and the PCT Theorem.
In this paper we generalize this picture in the following way. Firstly, given
a $\mathbb Z_2$-graded Lie group we define a (twisted-)local poset of abstract
wedge regions. We classify (semisimple) Lie algebras supporting abstract wedges
and study special wedge configurations. This allows us to exhibit an analog of
the Haag-Kastler one-particle net axioms for such general Lie groups without
referring to any specific spacetime. This set of axioms supports a first
quantization net obtained by generalizing the BGL construction. The
construction is possible for a large family of Lie groups and provides several
new models. We further comment on orthogonal wedges and extension of
symmetries.

Keywords:

algebraic quantum field theory, nets of standard subspaces, Lie groups, representation theory, Bisognano-Wichmann property