Symplectic Symmetries and Their Associated Hilbert Spaces

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Asghari Khonakdari, Ghazaleh | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50612 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Sheikh-Jabbari, Mohammad Mehdi; Rahvar, Sohrab
Abstract:
In every theory with local symmetries, observales are mainly the gauge invariant quantities and fields are defined up to a local transformation.By choosing boundary conditions on field configurations and on the generating functions of gauge transformations, we can associate conserved charges to a particular subset of the generating functions. Thus field combinations which are related by these particular gauge transformations are physically distinct. These set of conserved charges usually form infinite-dimensional algebras such as Virasoro or BMS algebra. In addition, sets of all combinations of the associated fields form a phase space with a symplectic structure induced form the action of the theory.In this thesis, we will study these phase spaces, their symmetries and the coadjoint orbits of these algebras. We also discuss quantization of the algebras and the associated Hilbert spaces and modules. In particular, we focus on Virasoro and BMS3 algebras and discuss how this viewpoint may remedy quantization of three dimensional gravity theories. We propose and briefly discuss spectral measure as a measure on the space of coadjoint orbits
Keywords:
Symplectic Symmety ; Hilbert Space ; Symplectic Spaces ; Symplectic Symmetries Orbits