Related papers: Combinatorial and topological phase structure of n…

Topological order is a new type order that beyond Landau's symmetry breaking theory. It has some interesting properties, such as producing quasi-particles with fractional quantum numbers and fractional/Fermi statistics, robust gapless…

We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…

This article gives an elementary account of the recently proposed theory of spontaneous quantum gravity. It is argued that a viable quantum theory of gravity should be falsifiable, and hence it should dynamically explain the observed…

We consider the quantum gravity partition function that counts the dimension of the Hilbert space of a spatial region with topology of a ball and fixed proper volume, and evaluate it in the leading order saddle point approximation. The…

I present a selective survey of the phases of quantum matter with varieties of many-particle quantum entanglement. I classify the phases as gapped, conformal, or compressible quantum matter. Gapped quantum matter is illustrated by a simple…

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…

In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main…

We use a mathematical framework that we introduced in a previous paper to study geometrical and quantum mechanical aspects of a Hall system with finite size and general boundary conditions. Geometrical structures control possibly the…

The talk is devoted to the "extended phase space" approach to Quantum Geometrodynamics. The premises that have led to the formulation of this approach are briefly reviewed, namely, non-trivial topology of the Universe which implies the…

We prove the equivalence in the covariant phase space of the metric and connection formulations for Palatini gravity, with nonmetricity and torsion, on a spacetime manifold with boundary. To this end, we will rely on the cohomological…

We consider non-chiral symmetry-protected topological phases of matter in two spatial dimensions protected by a discrete symmetry such as $\mathbb{Z}_K$ or $\mathbb Z_K \times \mathbb Z_K $ symmetry. We argue that modular…

Bargmann invariants and null phase curves are known to be important ingredients in understanding the essential nature of the geometric phase in quantum mechanics. Null phase manifolds in quantum-mechanical ray spaces are submanifolds made…

The nonadiabatic geometric phase in a time dependent quantum evolution is shown to provide an intrinsic concept of time having dual properties relative to the external time. A nontrivial extension of the ordinary quantum mechanics is thus…

We describe a theory of quantum gravity which is based on the assumption that the spacetime structure at small distances is given by a piecewise linear (PL) 4-manifold corresponding to a triangulation of a smooth 4-manifold. The fundamental…

We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…

Recent results obtained within a non-perturbative approach to quantum gravity based on the method of four-dimensional Causal Dynamical Triangulations are described. The phase diagram of the model consists of three phases. In the physically…

Phase space is the state space of classical mechanics, and this manifold is normally endowed only with a symplectic form. The geometry of quantum mechanics is necessarily more complicated. Arguments will be given to show that augmenting the…

Dynamical triangulations of four-dimensional Euclidean quantum gravity give rise to an interesting, numerically accessible model of quantum gravity. We give a simple introduction to the model and discuss two particularly important issues.…

We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…