The exact Wheeler-DeWitt equation for the scale-factor minisuperspace model
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910970885963776 |
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| author | Kaimakkamis, Eftychios Partouche, Hervé Sil, Karunava Toumbas, Nicolaos |
| author_facet | Kaimakkamis, Eftychios Partouche, Hervé Sil, Karunava Toumbas, Nicolaos |
| contents | We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum Hamiltonian leads to distinct Wheeler-DeWitt equations for the wavefunction $ψ$ of the Universe. Similarly, ambiguity arises in the path-integral formulation of $ψ$, due to the infinite choices of path-integral measures for the single degree of freedom of the model. For each choice of path-integral measure, we determine the correct operator ordering of the quantum Hamiltonian and derive the exact form of the Wheeler-DeWitt equation, including all corrections in $\hbar$. Additionally, we impose Hermiticity of the Hamiltonian to deduce the Hilbert-space measure $μ$, which appears in the definition of the Hermitian inner product. Remarkably, all quantum predictions can be expressed through the combination $Ψ=\sqrtμ\, ψ$, which satisfies a universal Wheeler-DeWitt equation, independent of the initial path-integral prescription. This result demonstrates that all seemingly distinct quantum theories arising from different quantization schemes of the same classical model are fundamentally equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The exact Wheeler-DeWitt equation for the scale-factor minisuperspace model Kaimakkamis, Eftychios Partouche, Hervé Sil, Karunava Toumbas, Nicolaos High Energy Physics - Theory General Relativity and Quantum Cosmology We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum Hamiltonian leads to distinct Wheeler-DeWitt equations for the wavefunction $ψ$ of the Universe. Similarly, ambiguity arises in the path-integral formulation of $ψ$, due to the infinite choices of path-integral measures for the single degree of freedom of the model. For each choice of path-integral measure, we determine the correct operator ordering of the quantum Hamiltonian and derive the exact form of the Wheeler-DeWitt equation, including all corrections in $\hbar$. Additionally, we impose Hermiticity of the Hamiltonian to deduce the Hilbert-space measure $μ$, which appears in the definition of the Hermitian inner product. Remarkably, all quantum predictions can be expressed through the combination $Ψ=\sqrtμ\, ψ$, which satisfies a universal Wheeler-DeWitt equation, independent of the initial path-integral prescription. This result demonstrates that all seemingly distinct quantum theories arising from different quantization schemes of the same classical model are fundamentally equivalent. |
| title | The exact Wheeler-DeWitt equation for the scale-factor minisuperspace model |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.18532 |