Related papers: Fermions on Quantum Geometry and Resolution of Dou…
We show that the quantization ambiguities of loop quantum cosmology, when considered in wider generality, can be used to produce discretionary dynamical behavior. There is an infinite dimensional space of ambiguities which parallels the…
Geometric properties of lattice quantum gravity in two dimensions are studied numerically via Monte Carlo on Euclidean Dynamical Triangulations. A new computational method is proposed to simulate gravity coupled with fermions, which allows…
We argue that a consistent coupling of a quantum theory to gravity requires an extension of ordinary `first order' Riemannian geometry to second order Riemannian geometry, which incorporates both a line element and an area element. This…
The interplay of geometric randomness and strong quantum fluctuations is an exciting topic in quantum many-body physics, leading to the emergence of novel quantum phases in strongly correlated electron systems. Recent investigations have…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
Modified dispersion relations (MDRs) arise in many quantum-gravity approaches, often in non-polynomial or non-analytic form beyond the reach of effective field theory (EFT). Logarithmic, exponential and trigonometric MDRs appear in causal…
We introduce the new problems of quantum packing, quantum covering, and quantum paving. These problems arise naturally when considering an algebra of non-commutative operators that is deeply rooted in quantum physics as well as in Gabor…
In perturbative QED, the approximation is improved by summing more Feynman graphs; in non-perturbative QCD, by refining the lattice. Here we observe that in quantum gravity the two procedures may well be the same. We outline the…
Quantum field theories at finite matter densities generically possess a partition function that is exponentially suppressed with the volume compared to that of the phase quenched analogue. The smallness arises from an almost uniform…
Requiring physical consistency in a classical flat spacetime geometrisation of fermions is shown to suggest the introduction of torsion. A resulting simple model for that torsion produces a localised quantum-like particle as a solution of a…
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…
We study geometric energy transport in a slowly driven single-level quantum dot weakly coupled to electronic contacts and with strong onsite interaction, which can be either repulsive or attractive. Exploiting a recently discovered…
Random-lattice fermions have been shown to be free of the doubling problem if there are no interactions or interactions of a non-gauge nature. However, gauge interactions impose stringent constraints as expressed by the Ward-Takahashi…
Strongly correlated Fermi systems are among the most intriguing, best experimentally studied and fundamental systems in physics. These are, however, in defiance of theoretical understanding. The ideas based on the concepts like Kondo…
This thesis discusses the topological aspects of quantum gravity, focusing on the connection between 2D quantum gravity and 2D topological gravity. The mathematical background for the discussion is presented in the first two chapters. The…
Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…
Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional…
We study the localization of fermions on a brane embedded in a space-time with $AdS_n \times M^k$ geometry. Quantum numbers of localized fermions are associated with their rotation momenta around the brane. Fermions with different quantum…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…