Quantum Scalar Field on Fuzzy de Sitter Space I. Field Modes and Vacua
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910368878559232 |
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| author | Brkic, Bojana Buric, Ilija Buric, Maja Latas, Dusko |
| author_facet | Brkic, Bojana Buric, Ilija Buric, Maja Latas, Dusko |
| contents | We study a scalar field on a noncommutative model of spacetime, the fuzzy de Sitter space, which is based on the algebra of the de Sitter group $SO(1,d)$ and its unitary irreducible representations. We solve the Klein-Gordon equation in $d=2,4$ and show, using a specific choice of coordinates and operator ordering, that all commutative field modes can be promoted to solutions of the fuzzy Klein-Gordon equation. To explore completeness of this set of modes, we specify a Hilbert space representation and study the matrix elements (integral kernels) of a scalar field: in this way the complete set of solutions of the fuzzy Klein-Gordon equation is found. The space of noncommutative solutions has more degrees of freedom than the commutative one, whenever spacetime dimension is $d>2$. In four dimensions, the new non-geometric, internal modes are parametrised by $S^2\times W$, where $W$ is a discrete matrix space. Our results pave the way to analysis of quantum field theory on the fuzzy de~Sitter space. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_10634 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Scalar Field on Fuzzy de Sitter Space I. Field Modes and Vacua Brkic, Bojana Buric, Ilija Buric, Maja Latas, Dusko High Energy Physics - Theory We study a scalar field on a noncommutative model of spacetime, the fuzzy de Sitter space, which is based on the algebra of the de Sitter group $SO(1,d)$ and its unitary irreducible representations. We solve the Klein-Gordon equation in $d=2,4$ and show, using a specific choice of coordinates and operator ordering, that all commutative field modes can be promoted to solutions of the fuzzy Klein-Gordon equation. To explore completeness of this set of modes, we specify a Hilbert space representation and study the matrix elements (integral kernels) of a scalar field: in this way the complete set of solutions of the fuzzy Klein-Gordon equation is found. The space of noncommutative solutions has more degrees of freedom than the commutative one, whenever spacetime dimension is $d>2$. In four dimensions, the new non-geometric, internal modes are parametrised by $S^2\times W$, where $W$ is a discrete matrix space. Our results pave the way to analysis of quantum field theory on the fuzzy de~Sitter space. |
| title | Quantum Scalar Field on Fuzzy de Sitter Space I. Field Modes and Vacua |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2403.10634 |