Geometrical Quantum Time in the $U(1)^3$ Model of Euclidean Quantum Gravity
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909408150159360 |
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| author | Bakhoda, Sepideh Ma, Yongge |
| author_facet | Bakhoda, Sepideh Ma, Yongge |
| contents | Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system exhibiting features similar to general relativity. By isolating a holonomy component within the Hamiltonian constraint, a discrete relative time evolution equation for quantum states is obtained. Then a Shrödinger-like equation is derived in continuous limit. Thus the physical states solving this Shrödinger-like equation can be written out. The emergence of the time parameter and its corresponding quantum operator are analyzed. It indicates the notion of a geometrical quantum time for quantum gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometrical Quantum Time in the $U(1)^3$ Model of Euclidean Quantum Gravity Bakhoda, Sepideh Ma, Yongge General Relativity and Quantum Cosmology High Energy Physics - Theory Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system exhibiting features similar to general relativity. By isolating a holonomy component within the Hamiltonian constraint, a discrete relative time evolution equation for quantum states is obtained. Then a Shrödinger-like equation is derived in continuous limit. Thus the physical states solving this Shrödinger-like equation can be written out. The emergence of the time parameter and its corresponding quantum operator are analyzed. It indicates the notion of a geometrical quantum time for quantum gravity. |
| title | Geometrical Quantum Time in the $U(1)^3$ Model of Euclidean Quantum Gravity |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2411.19435 |