A note on conformal symmetry
We investigate a conformal-like transformation for which the spacetime interval is invariant.
physics.gen-ph↗
arXiv subjects
D. N. Coumbe
Publications and source records attributed to D. N. Coumbe.
Renormalizing Spacetime
We propose that the consistent field renormalization of gravity requires a specific Weyl transformation of the metric tensor. As a consequence, proper length and time, as well as energy and momentum, become functions of scale. We estimate the functional form of the field renormalization factor by imposing a minimum resolvable distance scale under an infinitesimal Weyl transformation. The derived transformation is applied to two key problems in quantum gravity, its non-conformal scaling, and non-renormalizability.
physics.gen-ph↗
Exploring the new phase transition of CDT
This work focuses on the newly discovered bifurcation phase transition of CDT quantum gravity. We define various order parameters and investigate which is most suitable to study this transition in numerical simulations. By analyzing the behaviour of the order parameters we present evidence that the transition separating the bifurcation phase and the physical phase of CDT is likely a second or higher-order transition, a result that may have important implications for the continuum limit of CDT.
hep-th↗
Hypothesis on the Nature of Time
We present numerical evidence that fictitious diffusing particles in the causal dynamical triangulation (CDT) approach to quantum gravity exceed the speed of light on small distance scales. We argue this superluminal behaviour is responsible for the appearance of dimensional reduction in the spectral dimension. By axiomatically enforcing a scale invariant speed of light we show that time must dilate as a function of relative scale, just as it does as a function of relative velocity. By calculating the Hausdorff dimension of CDT diffusion paths we present a seemingly equivalent dual description in terms of a scale dependent Wick rotation of the metric. Such a modification to the nature of time may also have relevance for other approaches to quantum gravity.
gr-qc↗
Evidence for Asymptotic Safety from Dimensional Reduction in Causal Dynamical Triangulations
We calculate the spectral dimension for a nonperturbative lattice approach to quantum gravity, known as causal dynamical triangulations (CDT), showing that the dimension of spacetime smoothly decreases from approximately 4 on large distance scales to approximately 3/2 on small distance scales. This novel result may provide a possible resolution to a long-standing argument against the asymptotic safety scenario. A method for determining the relative lattice spacing within the physical phase of the CDT parameter space is also outlined, which might prove useful when studying renormalization group flow in models of lattice quantum gravity.
hep-th↗