Quantization of the Jackiw-Teitelboim model

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 SL(2,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 spacetime 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 depend 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.

Published version, a short note (not present in the published version) on the quantization of the null sector has been added

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Cited by in corpus (16)

• The Spin Foam Approach to Quantum Gravity
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• $BF$ gravity
• Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity
• $T\bar{T}$ in JT Gravity and BF Gauge Theory
• Jackiw-Teitelboim Gravity in the Second Order Formalism
• JT Gravity in de Sitter Space and the Problem of Time
• Tearing down spacetime with quantum disentanglement
• The Hilbert space of Chern-Simons theory on the cylinder. A Loop Quantum Gravity approach
• The new spin foam models and quantum gravity
• Two-dimensional gravity from vanishing metrical dimensions
• Constraint Analysis of Two-Dimensional Quadratic Gravity from BF Theory
• Massive fields and Wilson spools in JT gravity
• Aspects of Jackiw-Teitelboim Gravity in Anti-de Sitter and de Sitter spacetime
• Loop Quantization of the Supersymmetric Two-Dimensional BF Model