Partial absence of cosine problem in 3d Lorentzian spin foams
arXiv:2404.16943 · doi:10.1088/1361-6382/ad9700
Abstract
We study the semi-classical limit of the recently proposed coherent spin foam model for (2+1) Lorentzian quantum gravity. Specifically, we analyze the gluing equations derived from the stationary phase approximation of the vertex amplitude. Typically these exhibit two solutions yielding a cosine of the Regge action. However, by inspection of the algebraic equations as well as their geometrical realization, we show in this note that the behavior is more nuanced: when all triangles are either spacelike or timelike, two solutions exist. In any other case, only a single solution is obtained, thus yielding a single Regge exponential.
5 pages, 2 figures
References in corpus (26)
- LQG vertex with finite Immirzi parameter
- A new spinfoam vertex for quantum gravity
- A New Spin Foam Model for 4d Gravity
- The loop-quantum-gravity vertex-amplitude
- Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
- Lorentzian spin foam amplitudes: graphical calculus and asymptotics
- Asymptotic analysis of the EPRL four-simplex amplitude
- On the semiclassical limit of 4d spin foam models
- Graviton propagator from background-independent quantum gravity
- Complexifier Coherent States for Quantum General Relativity
- Coherent spin-networks
- SU(2) graph invariants, Regge actions and polytopes
- A spin foam model for general Lorentzian 4-geometries
- Implementing causality in the spin foam quantum geometry
- A Ponzano-Regge model of Lorentzian 3-Dimensional gravity
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity I - Convergence of multiple approaches and examples of Ponzano-Regge statistical duals
- Asymptotic analysis of spin foam amplitude with timelike triangles
- Asymptotic analysis of the EPRL model with timelike tetrahedra
- Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
- LQG propagator: III. The new vertex
- Spin foams with timelike surfaces
- Semiclassical Limits of Extended Racah Coefficients
- Asymptotic analysis of spin-foams with time-like faces in a new parameterisation
- The Lorentzian proper vertex amplitude: Asymptotics
- The Lorentzian proper vertex amplitude: Classical analysis and quantum derivation
- (2+1)-dimensional quantum gravity, spin networks and asymptotics