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.

Rindler楔形是AQFT中的基本本地化区域。它们由固定楔形的一组升压对称性参数确定。Brunetti–Guido–Longo（BGL）提供的自由场的代数典范构造来自楔升压识别，BW性质和PCT定理。在本文中，我们通过以下方式对此图片进行了概括。首先，给定一个\（\ mathbb Z_2 \）分级的李群，我们定义了一个抽象的楔形区域的（扭曲的）局部摆球。我们对支持抽象楔形的（半简单）李代数进行分类，并研究特殊的楔形配置。这使我们可以展示此类一般Lie群的Haag-Kastler单粒子净公理的类似物，而无需参考任何特定的时空。这套公理支持通过概括BGL构造而获得的第一量化网络。该构造对于一个大型Lie团体来说是可能的，并提供了几种新模型。我们进一步评论正交楔形和对称性的扩展。