Abstract
We study the phase space structure of the Jackiw-Teitelboim model in its connection variables formulation where the gauge group of the field theory is given by local $\mathrm{SL}(2,\mathbb{R})$ [or SU(2) for the Euclidean model], i.e. the de Sitter group in two dimensions. In order to make the connection with two-dimensional gravity explicit, a partial gauge fixing of the de Sitter symmetry can be introduced that reduces it to space-time diffeomorphisms. This can be done in different ways. Having no local physical degrees of freedom, the reduced phase space of the model is finite dimensional. The simplicity of this gauge field theory allows for studying different avenues for quantization, which may use various (partial) gauge fixings. We show that reduction and quantization are noncommuting operations: the representation of basic variables as operators in a Hilbert space depends on the order chosen for the latter. Moreover, a representation that is natural in one case may not even be available in the other leading to inequivalent quantum theories.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.