Abstract
In this work, we review 3-dimensional gravity by canonically analyzing the Hilbert-
Palatini action. We apply a time gauge used in 4-dimensional loop quantum gravity
[14] to the simpler case of the 3-dimensional loop quantum gravity. By time
gauge xing this Hilbert-Palatini action it leads to the Gauss constraints, the spatial
dieomorphism constraints, the Hamiltonian constraint and a new constraint
C. The gauge symmetries generated by this new constraints are spacetime dieomorphism
and SO(2) gauge transformations. We solve the dynamics of the theory
by providing a regularization of the generalized projector operator in terms of the
Hamiltonian constraint. We provide the denition of the physical scalar product
which can be represented in terms of a sum over nite spinfoam amplitudes. Then
we establish a clear-cut link between the canonical quantization of the new theory
to the spinfoam model (Ponzano-Regge model) dened in terms of the SU(2) spin
networks.
Osumanu, A (2021). Time Gauge Fixing For 3d Loop Quantum Gravity. Afribary. Retrieved from https://afribary.com/works/time-gauge-fixing-for-3d-loop-quantum-gravity
Osumanu, Abdulmajid "Time Gauge Fixing For 3d Loop Quantum Gravity" Afribary. Afribary, 14 Apr. 2021, https://afribary.com/works/time-gauge-fixing-for-3d-loop-quantum-gravity. Accessed 16 Nov. 2024.
Osumanu, Abdulmajid . "Time Gauge Fixing For 3d Loop Quantum Gravity". Afribary, Afribary, 14 Apr. 2021. Web. 16 Nov. 2024. < https://afribary.com/works/time-gauge-fixing-for-3d-loop-quantum-gravity >.
Osumanu, Abdulmajid . "Time Gauge Fixing For 3d Loop Quantum Gravity" Afribary (2021). Accessed November 16, 2024. https://afribary.com/works/time-gauge-fixing-for-3d-loop-quantum-gravity