Related papers: Topics in Quantum Geometry of Riemann Surfaces: Tw…
I briefly summarize recent results on classical and quantum dilaton gravity in 1+1 dimensions.
The purpose of these lectures is to discuss in some detail a new, non-perturbative approach to quantum gravity. I would like to present the basic ideas, outline the key results that have been obtained so far and indicate where we are headed…
Wolfgang Kummer was well known for his passion for axial gauges and for the formulation of gravity in terms of Cartan variables. The combination of the two applied to two dimensional dilaton gravity is the basis of the "Vienna School",…
Talk given at ICM '98, Berlin, reviewing some of the recent developments in understanding of string theory for a mathematical audience (to appear in Documenta Mathematica).
We study the quantum geometry of the fuzzy sphere defined as the angular momentum algebra $[x_i,x_j]=2\imath\lambda_p \epsilon_{ijk}x_k$ modulo setting $\sum_i x_i^2$ to a constant, using a recently introduced 3D rotationally invariant…
Two-dimensional electrodynamics coupled to Dirac fermions is mapped onto two-dimensional gravity in the first-order formalism, also including fermions. However, the resulting fermion-gravity coupling deviates from the conventional form,…
Some relations of the quantum potential to Weyl geometry are indicated with applications to the Friedmann equations for a toy quantum cosmology. Osmotic velocity and pressure are briefly discussed in terms of quantum mechanics and…
These lectures present a general critical assessment of various frameworks for quantum gravity, with particular emphasis on string theory. The topics discussed cover field-theoretical approaches to quantum gravity, anomalies, bosonic and…
Lectures presented at the Spring School, Trieste, Italy 1993.
General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt…
I give a brief overview of some Quantum-Gravity-Phenomenology research lines, focusing on studies of cosmic rays and gamma-ray bursts that concern the fate of Lorentz symmetry in quantum spacetime. I also stress that the most valuable…
Notes of five lectures given at the 2003 European School of High-Energy Physics, Tsakhkadzor, Armenia, September 2003
We develop a perturbation theory of four-dimensional topological 2-form gravity without cosmological constant. A 2-form and an $SU(2)$ connection 1-form are used as fundamental variables instead of metric. There is no quantum correction…
Lectures on Quantum Coulomb gases delivered at the CIME summer school on Quantum Many Body Systems 2010
These are lectures notes prepared for a series of seminars I am invited to give at Princeton Philosophy Department in November 2024. They cover the conceptual structure of quantum gravity, the relational interpretation of quantum mechanics,…
Over the last three years, a number of fundamental physical issues were addressed in loop quantum gravity. These include: A statistical mechanical derivation of the horizon entropy, encompassing astrophysically interesting black holes as…
Path integral quantization of generic two-dimensional dilaton gravity non-minimally coupled to a Dirac fermion is performed. After integrating out geometry exactly, perturbation theory is employed in the matter sector to derive the lowest…
We discuss some features of Einstein-Proca gravity in D=3 and 4 space-times. Our study includes a discussion on the tree-level unitarity and on the issue of light deflection in 3D gravity in the presence of a mass term.
We discuss the structure of one-loop counterterms for the two-dimensional theory of gravitation in the covariant scheme and study the effect of quantum reparametrizations.Some of them are shown to be equivalent to the introduction of…
We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under some mild topological assumptions, to a Gaussian fermionic system. In particular, for manifolds topologically equivalent to $\Sigma_g\times\RrR$ with $\Sigma_g$ a…