Quantum vacua, curved spacetime and singularities
| Thesis title in Czech: | Kvantová vakua, zakřivený prostoročas a singularity |
|---|---|
| Thesis title in English: | Quantum vacua, curved spacetime and singularities |
| Key words: | Weylova symmetrie|Weylova anomálie|Singularity|Geometrie and Topologie|Kanonická a Bogoliubova transformace|Kvantová neekvivalence |
| English key words: | Weyl symmetry|Weyl anomaly|Singularities|Geometry and Topology|Canonical and Bogoliubov transformation|Quantum inequivalence |
| Academic year of topic announcement: | 2022/2023 |
| Thesis type: | rigorosum thesis |
| Thesis language: | angličtina |
| Department: | Institute of Particle and Nuclear Physics (32-UCJF) |
| Supervisor: | prof. Alfredo Iorio, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 17.01.2023 |
| Date of assignment: | 17.01.2023 |
| Confirmed by Study dept. on: | 17.01.2023 |
| Date and time of defence: | 10.02.2023 00:00 |
| Date of electronic submission: | 17.01.2023 |
| Date of submission of printed version: | 17.01.2023 |
| Date of proceeded defence: | 10.02.2023 |
| Guidelines |
| The candidate will have knowledge of differential geometry and topology necessary to undertake studies of various spacetimes, with particular emphasis on three and two dimensional cases. She\He will also manage the basic formalism of Bogoliubov transformations and inequivalent quantization schemes. On the physics side, knowledge of spontaneous symmetry breaking, especially in its quantum version is welcome. Furthermore, during the work, knowledge of the defect-based gravity models will be built, along with simplified analog models of low-dimensional quantum fields in curved contexts. |
| References |
| R. d'Inverno, Introducing Einstein's Relativity, Clarendon Press (1990)
M.O. Katanaev, I.V. Volovich, Ann. Phys. 216 (1992) 1 N. Birrell, P. Davies, Quantum Fields in Curved Space, Cambridge University Press (1984) M. Nakahara, Geometry, Topology and Physics, Graduate Student Series in Physics, CRC Press (2003) L. P. Eisenhart, A treatise on the differential geometry of curves and surfaces, Princeton Univ. Press (1909) A. Ovchinnikov, in Nonlinearity and Geometry, D. Wojcik and J. Cieslinnski, Polish Scientific Publishers PWN (Warsaw) (1998) 41 Y. Takahashi, H. Umezawa, Thermofield Dynamics, Coll. Phen. 2 (1975) 55 H. Umezawa, Advanced Field Theory: Micro, Macro, and Thermal Physics, Amer. Inst. Phys. (1995) H.A. Kastrup, Fortsch. Phys. 51 (2003) 975 (quant-ph/0307069) A. Iorio, Alternative Symmetries in Quantum Field Theory and Gravity, arXiv:1102.5221 [hep-th] A. Iorio, Ann. Phys. 326 (2011) 1334-1353 A. Iorio, P. Pais, Phys. Rev. D 92 (2015) 125005 |
| Preliminary scope of work |
| The candidate will explore the relation among curvature of the spacetime, and the inequivalent quantizations/Hilbert spaces. In particular the focus will be on models that are, on the one hand simple (making the calculations potentially very explicit), on the other hand related to a topological-defect-based theory of gravity (making the emergence of topological inequivalence and singularities very explicit). One road that will be investigated is related to lower-dimensional cases, where conformal and Weyl symmetries play a crucial role. |