Quantum-reduced loop gravity: New perspectives on the kinematics and dynamics
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916502943301632 |
|---|---|
| author | Mäkinen, Ilkka |
| author_facet | Mäkinen, Ilkka |
| contents | We present a systematic approach to the kinematics of quantum-reduced loop gravity, a model originally proposed by Alesci and Cianfrani as an attempt to probe the physical implications of loop quantum gravity. We implement the quantum gauge-fixing procedure underlying quantum-reduced loop gravity by introducing a master constraint operator on the kinematical Hilbert space of loop quantum gravity, representing a set of gauge conditions which classically constrain the densitized triad to be diagonal. The standard Hilbert space of quantum-reduced loop gravity can be recovered as a space of solutions of the master constraint operator, while on the other hand the master constraint approach provides a useful starting point for considering possible generalizations of the standard construction. We also examine the quantum dynamics of states consisting of a single six-valent node in the quantum-reduced framework. We find that the Hamiltonian which governs the dynamics of such states bears a close formal resemblance to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum-reduced loop gravity: New perspectives on the kinematics and dynamics Mäkinen, Ilkka General Relativity and Quantum Cosmology We present a systematic approach to the kinematics of quantum-reduced loop gravity, a model originally proposed by Alesci and Cianfrani as an attempt to probe the physical implications of loop quantum gravity. We implement the quantum gauge-fixing procedure underlying quantum-reduced loop gravity by introducing a master constraint operator on the kinematical Hilbert space of loop quantum gravity, representing a set of gauge conditions which classically constrain the densitized triad to be diagonal. The standard Hilbert space of quantum-reduced loop gravity can be recovered as a space of solutions of the master constraint operator, while on the other hand the master constraint approach provides a useful starting point for considering possible generalizations of the standard construction. We also examine the quantum dynamics of states consisting of a single six-valent node in the quantum-reduced framework. We find that the Hamiltonian which governs the dynamics of such states bears a close formal resemblance to the Hamiltonian constraint of Bianchi I models in loop quantum cosmology. |
| title | Quantum-reduced loop gravity: New perspectives on the kinematics and dynamics |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.01368 |