EPRL/FK Asymptotics and the Flatness Problem
arXiv:1704.04817 · doi:10.1088/1361-6382/aaae82
Abstract
Spin foam models are an approach to quantum gravity based on the concept of sum over states, which aims to describe quantum spacetime dynamics in a way that its parent framework, loop quantum gravity, has not as of yet succeeded. Since these models' relation to classical Einstein gravity is not explicit, an important test of their viabilitiy is the study of asymptotics - the classical theory should be obtained in a limit where quantum effects are negligible, taken to be the limit of large triangle areas in a triangulated manifold with boundary. In this paper we will briefly introduce the EPRL/FK spin foam model and known results about its asymptotics, proceeding then to describe a practical computation of spin foam and semiclassical geometric data for a simple triangulation with only one interior triangle. The results are used to comment on the "flatness problem" - a hypothesis raised by Bonzom (2009) suggesting that EPRL/FK's classical limit only describes flat geometries in vacuum.
26 pages, 3 figures. Mathematica scripts for example calculations included in ancillary files
References in corpus (4)
Cited by in corpus (15)
- Effective Spin Foam Models for Four-Dimensional Quantum Gravity
- Effective Spin Foam Models for Lorentzian Quantum Gravity
- Numerical methods for EPRL spin foam transition amplitudes and Lorentzian recoupling theory
- A high-performance code for EPRL spin foam amplitudes
- Discrete gravity dynamics from effective spin foams
- Numerical analysis of spin foam dynamics and the flatness problem
- Addendum: EPRL/FK Asymptotics and the Flatness Problem
- From spin foams to area metric dynamics to gravitons
- Towards effective actions for the continuum limit of spin foams
- Quantum geometry from higher gauge theory
- Spin-foams as semi-classical vertices: gluing constraints and a hybrid algorithm
- Numerical evaluation of spin foam amplitudes beyond simplices
- Twisted geometries are area-metric geometries
- Curvature effects in the spectral dimension of spin foams
- Spinfoam tunneling of quantum geometries in angle variables