Covariant Homogeneous Nets of Standard Subspaces
Morinelli V, Neeb KH (2021)
Publication Type: Journal article
Publication year: 2021
Journal
DOI: 10.1007/s00220-021-04046-6
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 Theorem. 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.
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APA:
Morinelli, V., & Neeb, K.H. (2021). Covariant Homogeneous Nets of Standard Subspaces. Communications in Mathematical Physics. https://doi.org/10.1007/s00220-021-04046-6
MLA:
Morinelli, Vincenzo, and Karl Hermann Neeb. "Covariant Homogeneous Nets of Standard Subspaces." Communications in Mathematical Physics (2021).
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