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 The- orem. In this paper we generalize this picture in the following way. Firstly, given a Z2-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.
Covariant Homogeneous Nets of Standard Subspaces / Morinelli, Vincenzo; Neeb, Karl-Hermann. - In: COMMUNICATIONS IN MATHEMATICAL PHYSICS. - ISSN 0010-3616. - 386:1(2021), pp. 305-358. [10.1007/s00220-021-04046-6]
Covariant Homogeneous Nets of Standard Subspaces
Vincenzo Morinelli
;
2021
Abstract
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 The- orem. In this paper we generalize this picture in the following way. Firstly, given a Z2-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.File | Dimensione | Formato | |
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