Nets of real subspaces on homogeneous spaces and Algebraic Quantum Field Theory
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908648306900992 |
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| author | Neeb, Karl-Hermann |
| author_facet | Neeb, Karl-Hermann |
| contents | In these notes, we describe an interesting connection between unitary representations of Lie groups and nets of local algebras, as they appear in Algebraic Quantum Field Theory (AQFT). It is based on first translating the axioms for nets of operator algebras parameterized by regions in a space-time manifold into those for nets of real subspaces, and then study this structure from a perspective based on geometry and representation theory of Lie groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_09360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nets of real subspaces on homogeneous spaces and Algebraic Quantum Field Theory Neeb, Karl-Hermann Operator Algebras Mathematical Physics Representation Theory 81T05, 22E44 In these notes, we describe an interesting connection between unitary representations of Lie groups and nets of local algebras, as they appear in Algebraic Quantum Field Theory (AQFT). It is based on first translating the axioms for nets of operator algebras parameterized by regions in a space-time manifold into those for nets of real subspaces, and then study this structure from a perspective based on geometry and representation theory of Lie groups. |
| title | Nets of real subspaces on homogeneous spaces and Algebraic Quantum Field Theory |
| topic | Operator Algebras Mathematical Physics Representation Theory 81T05, 22E44 |
| url | https://arxiv.org/abs/2511.09360 |