Related papers: Generalised spectral dimensions in non-perturbativ…
The spectrum of the Laplace-Beltrami operator, computed on the spatial slices of Causal Dynamical Triangulations, is a powerful probe of the geometrical properties of the configurations sampled in the various phases of the lattice theory.…
Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter…
Results that illuminate the physical interpretation of states of nonperturbative quantum gravity are obtained using the recently introduced loop variables. It is shown that: i) While local operators such as the metric at a point may not be…
The critical behavior of infinite families of shift symmetric interacting theories with higher derivative kinetic terms (non unitary) is considered. Single scalar theories with shift symmetry are classified according to their upper critical…
The two dimensional substructure of general relativity and gravity, and the two dimensional geometry of quantum effect by black hole are disclosed. Then the canonical quantization of the two dimensional theory of gravity is performed. It is…
The possible interpretations of a new continuum model for the two-dimensional quantum gravity for $d>1$ ($d$=matter central charge), obtained by carefully treating both diffeomorphism and Weyl symmetries, are discussed. In particular we…
In this paper we study ensembles of finite real spectral triples equipped with a path integral over the space of possible Dirac operators. In the noncommutative geometric setting of spectral triples, Dirac operators take the center stage as…
We investigate the effective field theory of a quantum chaotic billiard from a new perspective of quantum anomalies, which result from the absence of continuous spectral symmetry in quantized systems. It is shown that commutators of…
We study some phenomenological implications of models where the scale of quantum gravity effects lies much below the four-dimensional Planck scale. These models arise from M-theory vacua where either the internal space volume is large or…
It is conjectured that the spatial structure of quantum field states is influenced by a new kind of directional indeterminacy of quantum geometry set by the Planck length, $l_P$, that does not occur in a classical background geometry.…
This paper is committed to calculations near a type of future singularity driven by phantom energy. At the singularities considered, the scale factor remains finite but its derivative diverges. The general behavior of barotropic phantom…
We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
We study quantum effects in higher curvature extensions of general relativity using the functional renormalisation group. New flow equations are derived for general classes of models involving Ricci scalar, Ricci tensor, and Riemann tensor…
A viable quantum theory of gravity is one of the biggest challenges facing physicists. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity --…
The Mabuchi energy is an interesting geometric functional on the space of K\"ahler metrics that plays a crucial r\^ole in the study of the geometry of K\"ahler manifolds. We show that this functional, as well as other related geometric…
Fundamental scale invariance implies the scale invariant standard model. Both the Fermi scale and the Planck mass are given by fields, and their ratio is dictated by a dimensionless cosmon-Higgs coupling. For an ultraviolet fixed point of…
Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature…
Quantum mechanics in a noncommutative plane is considered. For a general two dimensional central field, we find that the theory can be perturbatively solved for large values of the noncommutative parameter ($\theta$) and explicit…
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…