The Role of Type $II_{\infty}$ v.Neumann Algebras and their Tensor Structure in Quantum Gravity}}
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915097287327744 |
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| author | Requardt, Manfred |
| author_facet | Requardt, Manfred |
| contents | We will argue in this paper that the type classification of v.Neumann algebras play an important role in a theory of quantum gravity and quantum space-time physics. We provide arguments that type $II_{\infty}$ and its representation as a tensor product of an ordinary (exterior) Hilbert space algebra $\cB(\cH_I)$ and an (internal) type $II_1$ algebra, encoding, in our view, the hidden microscopic gravitational degrees of freedom, do represent the first step away from the semiclassical picture towards a full theory of quantum gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06009 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Role of Type $II_{\infty}$ v.Neumann Algebras and their Tensor Structure in Quantum Gravity}} Requardt, Manfred General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We will argue in this paper that the type classification of v.Neumann algebras play an important role in a theory of quantum gravity and quantum space-time physics. We provide arguments that type $II_{\infty}$ and its representation as a tensor product of an ordinary (exterior) Hilbert space algebra $\cB(\cH_I)$ and an (internal) type $II_1$ algebra, encoding, in our view, the hidden microscopic gravitational degrees of freedom, do represent the first step away from the semiclassical picture towards a full theory of quantum gravity. |
| title | The Role of Type $II_{\infty}$ v.Neumann Algebras and their Tensor Structure in Quantum Gravity}} |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2501.06009 |