Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals
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| Autores principales: | , , , |
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| Formato: | Preprint |
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2024
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| _version_ | 1866929653041594368 |
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| author | Camblong, H. E. Chakraborty, A. Lopez-Duque, P. Ordóñez, C. R. |
| author_facet | Camblong, H. E. Chakraborty, A. Lopez-Duque, P. Ordóñez, C. R. |
| contents | An observer with a finite lifetime $\mathcal{T}$ perceives the Minkowski vacuum as a thermal state at temperature $T_D = 2 \hbar/(π\mathcal{T})$, as a result of being constrained to a double-coned-shaped region known as a causal diamond. In this paper, we explore the emergence of thermality in causal diamonds due to the role played by the symmetries of conformal quantum mechanics (CQM) as a (0+1)-dimensional conformal field theory, within the de Alfaro-Fubini-Furlan model and generalizations. In this context, the hyperbolic operator $S$ of the SO(2,1) symmetry of CQM: (i) is the generator of the time evolution of a diamond observer; (ii) its dynamical behavior leads to the predicted thermal nature; and (iii) its associated quantum instability has a Lyapunov exponent $λ_L = πT_D/\hbar$, which is half the upper saturation bound of the information scrambling rate. Our approach is based on a comprehensive framework of path-integral representations of the CQM generators in canonical and microcanonical forms, supplemented by semiclassical arguments. The properties of the operator $S$ are studied with emphasis on an operator duality with the corresponding elliptic operator $R$, using a representation in terms of an effective scale-invariant inverse square potential combined with inverted and ordinary harmonic oscillator potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals Camblong, H. E. Chakraborty, A. Lopez-Duque, P. Ordóñez, C. R. Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics An observer with a finite lifetime $\mathcal{T}$ perceives the Minkowski vacuum as a thermal state at temperature $T_D = 2 \hbar/(π\mathcal{T})$, as a result of being constrained to a double-coned-shaped region known as a causal diamond. In this paper, we explore the emergence of thermality in causal diamonds due to the role played by the symmetries of conformal quantum mechanics (CQM) as a (0+1)-dimensional conformal field theory, within the de Alfaro-Fubini-Furlan model and generalizations. In this context, the hyperbolic operator $S$ of the SO(2,1) symmetry of CQM: (i) is the generator of the time evolution of a diamond observer; (ii) its dynamical behavior leads to the predicted thermal nature; and (iii) its associated quantum instability has a Lyapunov exponent $λ_L = πT_D/\hbar$, which is half the upper saturation bound of the information scrambling rate. Our approach is based on a comprehensive framework of path-integral representations of the CQM generators in canonical and microcanonical forms, supplemented by semiclassical arguments. The properties of the operator $S$ are studied with emphasis on an operator duality with the corresponding elliptic operator $R$, using a representation in terms of an effective scale-invariant inverse square potential combined with inverted and ordinary harmonic oscillator potentials. |
| title | Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals |
| topic | Quantum Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2407.18177 |