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1	Moduli spaces and deformation quantization in infinite dimensions Fedosov, Boris January 1998 (has links) We construct a deformation quantization on an infinite-dimensional symplectic space of regular connections on an SU(2)-bundle over a Riemannian surface of genus g ≥ 2. The construction is based on the normal form thoerem representing the space of connections as a fibration over a finite-dimensional moduli space of flat connections whose fibre is a cotangent bundle of the infinite-dimensional gauge group. We study the reduction with respect to the gauge groupe both for classical and quantum cases and show that our quantization commutes with reduction. moduli space of flat connections gauge group star-product Weyl algebras bundle symplectic reduction Mathematics
2	Quantum gravity in two- and three-dimensional dS spaces Chernichenko, Alexsey January 2024 (has links) This thesis is a study of certain aspects of quantum gravity in two- and three-dimensional de Sitter spaces. The model used in dS2 is the Jackiw- Tetitelboim gravity which involves a scalar coupling. At low-energy limit this model becomes Schwarzian theory for which one can compute one-loop partition function. Along the way, the model is recasted into the first order formalism which helps to find an appropriate measure for the partition function. The layout for quantum gravity in dS3 is practically the same and many results appear to be quite similar. Although, there are as many dissimilarities. Ultimately, the goal is different, namely to determine one-loop correction to the central charge of the theory dual to dS3 . Additionally, a putative genus expansion for Jackiw-Teitelboim gravity is investigated along with some concrete computations being done. / Detta examensarbete ̈ar en studie av vissa aspekter av kvantgravita-tion i två och tredimensionella de Sitter-rummen. Den behandlar Jackiw-Teitelboim gravitation i dS2 , en model med en skalär koppling. Vid lågenergigränns blir modellen till Schwarzian teorin som används för att beräkna första ordningskorrektionen till partitionsfunktion. På vägen dit skrivs om modelen till första ordningens formalism som sedan hjälper att hitta ett lämpligt mått för partitionsfunktionen. Plannen för dS3 ser ut i princip likadant och en stor del av resultater är liknande. Emellertid finns det lika många olikheter. I slut änden, målet är annorludna, nämligen att beräkna första ordningens korrektion till centrala laddningen av teorin som dual till dS3 . Dessutom, en förmodad genus expansion för Jackiw-Teitelboim gravitation är undersökt och vissa konkreta beräkningar är gjorda. Gravity Quantum gravity de Sitter space Jackiw-Teitelboim gravity Hartle-Hawking wavefunction of the Universe Wheeler-DeWitt equation Gravitational path integral Partition function Dilaton Gibbons-Hawking-York term Schwarzian theory Flat connections Space of flat connections Symplectic form Symplectic measure Holonomy Monodromy Genus expansion Weil-Peterson volumes Mirzakhani's recursion formula Central charge Chern-Simons theory Wess-Zumino-Witten model Natural Sciences Naturvetenskap Physical Sciences Fysik

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Moduli spaces and deformation quantization in infinite dimensions

Quantum gravity in two- and three-dimensional dS spaces