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Four-dimensional Spinfoam Quantum Gravity with Cosmological Constant: Finiteness and Semiclassical Limit
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abstract
We present an improved formulation of 4-dimensional Lorentzian spinfoam quantum gravity with cosmological constant. The construction of spinfoam amplitudes uses the state-integral model of PSL(2,$\mathbb{C}$) Chern-Simons theory and the implementation of simplicity constraint. The formulation has 2 key features: (1) spinfoam amplitudes are all finite, and (2) With suitable boundary data, the semiclassical asymptotics of the vertex amplitude has two oscillatory terms, with phase plus or minus the 4-dimensional Lorentzian Regge action with cosmological constant for the constant curvature 4-simplex.
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The one-loop effective action from the coherent state path integral of loop quantum gravity
The one-loop effective action from the LQG coherent state path integral is computed and found to be UV-finite, with the dynamical area j0 > 0 at the quantum level.
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