Related papers: The transfer matrix in four-dimensional Causal Dyn…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
These lecture notes introduce quantum spin systems and several computational methods for studying their ground-state and finite-temperature properties. Symmetry-breaking and critical phenomena are first discussed in the simpler setting of…
One could begin a study like the present one by simply postulating that our universe is four-dimensional. There are ample reasons for doing this. Experience, observation and experiment all point to the fact that we inhabit a…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
Is there an approach to quantum gravity which is conceptually simple, relies on very few fundamental physical principles and ingredients, emphasizes geometric (as opposed to algebraic) properties, comes with a definite numerical…
We discuss the algorithmic problem of minimal coupling gauge fields of the Yang-Mills type to Quantum Gravity in the approach known as Causal Dynamical Triangulations (CDT) as a step towards studying, ultimately, systems of gravity coupled…
Generalized causal dynamical triangulations (generalized CDT) is a model of two-dimensional quantum gravity in which a limited number of spatial topology changes is allowed to occur. We solve the model at the discretized level using…
Three-dimensional Lorentzian quantum gravity, expressed as the continuum limit of a nonperturbative sum over spacetimes, is tantalizingly close to being amenable to analytical methods, and some of its properties have been described in terms…
Recently a matrix model with non-pairwise index contractions has been studied in the context of the canonical tensor model, a tensor model for quantum gravity in the canonical formalism. This matrix model also appears in the same form with…
Four-dimensional simplicial quantum gravity is modified either by coupling it to U(1) gauge fields or by introducing a measure weighted by the orders of the triangles. Strong coupling expansion and Monte Carlo simulations are used. Although…
The trace anomaly induced dynamics of the conformal factor is investigated in four-dimensional quantum gravity with torsion. The constraints for the coupling constants of torsion matter interaction are obtained in the infrared stable fixed…
This article discusses the infrared and the (perspective) ultraviolet limits of four-dimensional Causal Dynamical Triangulations (CDT). CDT is a non-perturabtive and background-independent approach to quantization of Einstein's gravity,…
We discuss scaling relations in four dimensional simplicial quantum gravity. Using numerical results obtained with a new algorithm called ``baby universe surgery'' we study the critical region of the theory. The position of the phase…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
We study the geometries generated by two-dimensional causal dynamical triangulations (CDT) coupled to $d$ massless scalar fields. Using methods similar to those used to study four-dimensional CDT we show that there exists a $c=1$ "barrier",…
We introduce a transfer matrix formalism for the (annealed) Ising model coupled to two-dimensional causal dynamical triangulations. Using the Krein-Rutman theory of positivity preserving operators we study several properties of the emerging…
We employ machine learning techniques to provide accurate variational wavefunctions for matrix quantum mechanics, with multiple bosonic and fermionic matrices. Variational quantum Monte Carlo is implemented with deep generative flows to…
We investigate the impact of spatial topology in 3+1 dimensional causal dynamical triangulations (CDT) by performing numerical simulations with toroidal spatial topology instead of the previously used spherical topology. In the case of…
We present a detailed analysis of a recently introduced version of Causal Dynamical Triangulations (CDT) that does not rely on a distinguished time slicing. Focussing on the case of 2+1 spacetime dimensions, we analyze its geometric and…
This letter discusses phenomenological aspects of dimensional reduction predicted by the Causal Dynamical Triangulations (CDT) approach to quantum gravity. The deformed form of the dispersion relation for the fields defined on the CDT…