Quantum Effective Dynamics and Stability of Vacuum in Anti-de Sitter Spacetimes
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arXiv
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| Formato: | Preprint |
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2026
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| _version_ | 1866912884410286080 |
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| author | Li, Shi-Yuan Liu, Chengwu |
| author_facet | Li, Shi-Yuan Liu, Chengwu |
| contents | We investigate the details of the canonical quantization of effective quantum field theories in anti-de Sitter spacetime, emphasizing the stability of the quantum vacuum. We take the scalar and Maxwell fields as examples. For the non-minimally coupled massless real scalar field with ξRϕ^2 term in the Lagrangian (mass can be introduced by shift of ξ), only when ξ\le 5/48, the quantized Hamiltonian is spontaneously non-negative and the vacuum is well defined. For ξ> 5/48, one has to assign the negative energy spectrum as that of the ghost particles, introducing anti-commutation relations to make the corresponding part of the Hamiltonian trivial, ensuring the Hamiltonian non-negative and the vacuum (and the Hilbert space) well defined. This method of ghost states is applicable once the proper radial boundary conditions guarantee the Hamiltonian self-adjoint. The resulting dynamics can be compared with those resulting from the positive self-adjoint extensions when the latter is available for ξ\le 9/48. For the Maxwell fields, the gauge invariant canonical energy momentum tensor straightforwardly leads to the gauge invariant non-negative Hamiltonian (well-defined vacuum). Hence the redundant gauge degree of freedom is irrelevant, and the 2-dimensional dynamical degrees of freedom are quantized in a concrete, e.g., temporal gauge. The energy momentum tensors for both quantized fields are renormalized to be finite at operator level, which renders the stable vacuum maximally symmetric. The back-reactions to the background spacetime by excited states via the semi-classical Einstein equations are also discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_06583 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Effective Dynamics and Stability of Vacuum in Anti-de Sitter Spacetimes Li, Shi-Yuan Liu, Chengwu General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory We investigate the details of the canonical quantization of effective quantum field theories in anti-de Sitter spacetime, emphasizing the stability of the quantum vacuum. We take the scalar and Maxwell fields as examples. For the non-minimally coupled massless real scalar field with ξRϕ^2 term in the Lagrangian (mass can be introduced by shift of ξ), only when ξ\le 5/48, the quantized Hamiltonian is spontaneously non-negative and the vacuum is well defined. For ξ> 5/48, one has to assign the negative energy spectrum as that of the ghost particles, introducing anti-commutation relations to make the corresponding part of the Hamiltonian trivial, ensuring the Hamiltonian non-negative and the vacuum (and the Hilbert space) well defined. This method of ghost states is applicable once the proper radial boundary conditions guarantee the Hamiltonian self-adjoint. The resulting dynamics can be compared with those resulting from the positive self-adjoint extensions when the latter is available for ξ\le 9/48. For the Maxwell fields, the gauge invariant canonical energy momentum tensor straightforwardly leads to the gauge invariant non-negative Hamiltonian (well-defined vacuum). Hence the redundant gauge degree of freedom is irrelevant, and the 2-dimensional dynamical degrees of freedom are quantized in a concrete, e.g., temporal gauge. The energy momentum tensors for both quantized fields are renormalized to be finite at operator level, which renders the stable vacuum maximally symmetric. The back-reactions to the background spacetime by excited states via the semi-classical Einstein equations are also discussed. |
| title | Quantum Effective Dynamics and Stability of Vacuum in Anti-de Sitter Spacetimes |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2602.06583 |