Fri - 07/05/24

**Title:

      Quantum Curved Tetrahedron, Quantum Group Intertwiner Space, and Coherent States**  - **Authors:** Chen-Hung Hsiao, Qiaoyin Pan  - **Subjects:** Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  In this paper, we construct the phase space of a constantly curved tetrahedron with fixed triangle areas in terms of a pair of Darboux coordinates called the length and twist coordinates, which are in analogy to the Fenchel-Nielsen coordinates for flat connections, and their quantization. The curvature is identified to the value of the cosmological constant, either positive or negative. The physical Hilbert space is given by the $\mathcal{U}_q(\mathfrak{su}(2))$ intertwiner space. We show that the quantum trace of quantum monodromies, defining the quantum length operators, form a fusion algebra and describe their representation theory. We also construct the coherent states in the physical Hilbert space labeled by the length and twist coordinates. These coherent states describe quantum curved tetrahedra and peak at points of the tetrahedron phase space. This works is closely related to 3+1 dimensional Loop Quantum Gravity with a non-vanishing cosmological constant. The coherent states constructed herein serve as good candidates for the application to the spinfoam model with a cosmological constant.

**Title:

      Quantum Curved Tetrahedron, Quantum Group Intertwiner Space, and Coherent States**  - **Authors:** Chen-Hung Hsiao, Qiaoyin Pan  - **Subjects:** Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  In this paper, we construct the phase space of a constantly curved tetrahedron with fixed triangle areas in terms of a pair of Darboux coordinates called the length and twist coordinates, which are in analogy to the Fenchel-Nielsen coordinates for flat connections, and their quantization. The curvature is identified to the value of the cosmological constant, either positive or negative. The physical Hilbert space is given by the $\mathcal{U}_q(\mathfrak{su}(2))$ intertwiner space. We show that the quantum trace of quantum monodromies, defining the quantum length operators, form a fusion algebra and describe their representation theory. We also construct the coherent states in the physical Hilbert space labeled by the length and twist coordinates. These coherent states describe quantum curved tetrahedra and peak at points of the tetrahedron phase space. This works is closely related to 3+1 dimensional Loop Quantum Gravity with a non-vanishing cosmological constant. The coherent states constructed herein serve as good candidates for the application to the spinfoam model with a cosmological constant.
  1. [] - Title: Entangled pairs in evaporating black holes without event horizons - Ivan Agullo, Paula Calizaya Cabrera, Beatriz Elizaga Navascués

Thu - 07/04/24

**Title:

      Quantum Curved Tetrahedron, Quantum Group Intertwiner Space, and Coherent States**  - **Authors:** Chen-Hung Hsiao, Qiaoyin Pan  - **Subjects:** Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  In this paper, we construct the phase space of a constantly curved tetrahedron with fixed triangle areas in terms of a pair of Darboux coordinates called the length and twist coordinates, which are in analogy to the Fenchel-Nielsen coordinates for flat connections, and their quantization. The curvature is identified to the value of the cosmological constant, either positive or negative. The physical Hilbert space is given by the $\mathcal{U}_q(\mathfrak{su}(2))$ intertwiner space. We show that the quantum trace of quantum monodromies, defining the quantum length operators, form a fusion algebra and describe their representation theory. We also construct the coherent states in the physical Hilbert space labeled by the length and twist coordinates. These coherent states describe quantum curved tetrahedra and peak at points of the tetrahedron phase space. This works is closely related to 3+1 dimensional Loop Quantum Gravity with a non-vanishing cosmological constant. The coherent states constructed herein serve as good candidates for the application to the spinfoam model with a cosmological constant.

**Title:

      Quantum Curved Tetrahedron, Quantum Group Intertwiner Space, and Coherent States**  - **Authors:** Chen-Hung Hsiao, Qiaoyin Pan  - **Subjects:** Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  In this paper, we construct the phase space of a constantly curved tetrahedron with fixed triangle areas in terms of a pair of Darboux coordinates called the length and twist coordinates, which are in analogy to the Fenchel-Nielsen coordinates for flat connections, and their quantization. The curvature is identified to the value of the cosmological constant, either positive or negative. The physical Hilbert space is given by the $\mathcal{U}_q(\mathfrak{su}(2))$ intertwiner space. We show that the quantum trace of quantum monodromies, defining the quantum length operators, form a fusion algebra and describe their representation theory. We also construct the coherent states in the physical Hilbert space labeled by the length and twist coordinates. These coherent states describe quantum curved tetrahedra and peak at points of the tetrahedron phase space. This works is closely related to 3+1 dimensional Loop Quantum Gravity with a non-vanishing cosmological constant. The coherent states constructed herein serve as good candidates for the application to the spinfoam model with a cosmological constant.
  1. [] - Title: Entangled pairs in evaporating black holes without event horizons - Ivan Agullo, Paula Calizaya Cabrera, Beatriz Elizaga Navascués

Wed - 07/03/24

**Title:

      Gravitational waveforms from periodic orbits around a quantum-corrected black hole**  - **Authors:** Sen Yang, Yu-Peng Zhang, Tao Zhu, Li Zhao, Yu-Xiao Liu  - **Subjects:** Subjects: General Relativity and Quantum Cosmology (gr-qc)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  Extreme mass-ratio inspirals are crucial sources for future space-based gravitational wave detections. Gravitational waveforms emitted by extreme mass-ratio inspirals are closely related to the orbital dynamics of small celestial objects, which vary with the underlying spacetime geometry. Despite the tremendous success of general relativity, there are unsolved issues such as singularities in both black holes and cosmology. Loop quantum gravity, a theory addressing these singularity problems, offers a framework for regular black holes. In this paper, we focus on periodic orbits of a small celestial object around a supermassive quantum-corrected black hole in loop quantum gravity and compute the corresponding gravitational waveforms. We view the small celestial object as a massive test particle and obtain its four-velocity and effective potential. Our results indicate that the quantum parameter $\hat{\alpha}$ influences the shape of the effective potential. We explore the effects of quantum corrections on marginally bound orbits, innermost stable circular orbits, and other periodic orbits. Using the numerical kludge scheme, we further explore the gravitational waveforms of the small celestial object along different periodic orbits. The waveforms exhibit distinct zoom and whirl phases in a complete orbital period, closely tied to the quantum parameter $\hat{\alpha}$. We also perform a spectral analysis of the gravitational waves from these periodic orbits and assess their detectability. With the steady progress of space-based gravitational wave detection programs, our findings will contribute to utilizing extreme mass-ratio inspirals to test and understand the properties of quantum-corrected black holes.

There is no new related paper today

Tue - 07/02/24

There is no new related paper today

**Title:

      Efficient Tensor Network Algorithms for Spin Foam Models**  - **Authors:** Seth K. Asante, Sebastian Steinhaus  - **Subjects:** Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  Numerical computations and methods have become increasingly crucial in the study of spin foam models across various regimes. This paper adds to this field by introducing new algorithms based on tensor network methods for computing amplitudes, focusing on topological SU(2) BF and Lorentzian EPRL spin foam models. By reorganizing the sums and tensors involved, vertex amplitudes are recast as a sequence of matrix contractions. This reorganization significantly reduces computational complexity and memory usage, allowing for scalable and efficient computations of the amplitudes for larger representation labels on standard consumer hardware--previously infeasible due to the computational demands of high-valent tensors. We apply these tensor network algorithms to analyze the characteristics of various vertex configurations, including Regge and vector geometries for the SU(2) BF theory, demonstrating consistent scaling behavior and differing oscillation patterns. Our benchmarks reveal substantial improvements in computational time and memory allocations, especially for large representation labels. Additionally, these tensor network methods are applicable to generic 2-complexes with multiple vertices, where we introduce partial-coherent vertex amplitudes to streamline the computations. The implementation of these algorithms is available on GitHub for further exploration and use.

Mon - 07/01/24

There is no new related paper today

**Title:

      Efficient Tensor Network Algorithms for Spin Foam Models**  - **Authors:** Seth K. Asante, Sebastian Steinhaus  - **Subjects:** Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)  - **Arxiv link:** [https://arxiv.org/abs/](https://arxiv.org/abs/)  - **Abstract**  Numerical computations and methods have become increasingly crucial in the study of spin foam models across various regimes. This paper adds to this field by introducing new algorithms based on tensor network methods for computing amplitudes, focusing on topological SU(2) BF and Lorentzian EPRL spin foam models. By reorganizing the sums and tensors involved, vertex amplitudes are recast as a sequence of matrix contractions. This reorganization significantly reduces computational complexity and memory usage, allowing for scalable and efficient computations of the amplitudes for larger representation labels on standard consumer hardware--previously infeasible due to the computational demands of high-valent tensors. We apply these tensor network algorithms to analyze the characteristics of various vertex configurations, including Regge and vector geometries for the SU(2) BF theory, demonstrating consistent scaling behavior and differing oscillation patterns. Our benchmarks reveal substantial improvements in computational time and memory allocations, especially for large representation labels. Additionally, these tensor network methods are applicable to generic 2-complexes with multiple vertices, where we introduce partial-coherent vertex amplitudes to streamline the computations. The implementation of these algorithms is available on GitHub for further exploration and use.

New papers last week