Related papers: Quantum Graphity
Quantum gravity that describes the world beyond the Planck scale should be formulated in a background-metric independent manner. Such a background-free nature can be represented as a gauge equivalency under conformal transformations, called…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…
We explore the extension of quantum cosmology outside the homogeneous approximation, using the formalism of loop quantum gravity. We introduce a model where some of the inhomogeneous degrees of freedom are present, providing a tool for…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
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…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…
The phenomenon of quantum phase transition is considered in the special case in which the evolution laws remain unitary and in which the bound-state energies remain observable. The conventional Hermiticity of observables is lost at the…
We investigate the possibility that a background independent quantum theory of gravity is not a theory of quantum geometry. We provide a way for global spacetime symmetries to emerge from a background independent theory without geometry. In…
It is generally believed that a full-fledged theory of quantum gravity should exhibit background independence and diffeomorphism invariance. In its most general form, the latter comprises field redefinitions, which are diffeomorphisms in…
We discuss phenomenology of quantum vacuum. Phenomenology of macroscopic systems has three sources: thermodynamics, topology and symmetry. Momentum space topology determines the universality classes of fermionic vacua. The vacuum in its…
A graph theoretic perspective is taken for a range of phenomena in continuum physics in order to develop representations for analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena described by partial…
So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the…
The description of states and dynamics in non-Hermitian systems is fundamentally linked to the choice of an appropriate theoretical framework -- a point of ongoing debate in the field. This work addresses this issue by proposing a…
Recently some hidden inconsistencies in high energy physics and cosmology have been articulated by several scholars. If we follow the usual description we get an unacceptably high cosmological constant as was noticed by Weinberg and others…
We present, theoretical predictions and Monte Carlo simulations, for a simple three matrix model that exhibits an exotic phase transition. The nature of the transition is very different if approached from the high or low temperature side.…
We study a scenario for the very early universe in which there is a fast phase transition from a non-geometric, high temperature phase to a low temperature, geometric phase described by a classical solution to the Einstein equations. In…
We explore quantum mechanical theories whose fundamental degrees of freedom are rectangular matrices with Grassmann valued matrix elements. We study particular models where the low energy sector can be described in terms of a bosonic…
(2+1) dimensional gravity is equivalent to an exactly soluble non-Abelian Chern-Simons gauge field theory (E Witten 1988). Regarding this as the topological phase of quantum gravity in (2+1)d, we suggest a topological symmetry breaking by…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
The recently proposed theory of "Asymptotically Free Mimetic Gravity" is extended to the general non-homogeneous, spatially non-flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this…