Related papers: Topics in Quantum Geometry of Riemann Surfaces: Tw…
Lecture notes from the Third International School on Geometry and Physics at the Centre de Recerca Matematica in Barcelona, March 26--30, 2012.
We review quantum gravity model building using the new formalism of `quantum Riemannian geometry' to construct this on finite discrete spaces and on fuzzy ones such as matrix algebras. The formalism starts with a `differential structure' as…
In 1927, just after he obtained a full professorship, Enrico Fermi delivered his first course on Theoretical Physics at the Institute of Physics in Rome. The following year Edoardo Amaldi, Emilio Segre' and Ettore Majorana became students…
This review is based on lectures given at the 1992 Trieste Spring School on String Theory and Quantum Gravity and at the 1992 TASI Summer School in Boulder, Colorado.
We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic…
As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of…
Four pedagogical Lectures at the NATO-ASI on "Quantum Geometry" in Akureyri, Iceland, August 1999. Contents: 1. O(N) Vector Models, 2. Large-N QCD, 3. QCD in Loop Space, 4. Large-N Reduction
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…
In April 1925, Enrico Fermi was only 23 years old and he had graduated less than three years earlier. Despite his age, Fermi was invited at the University of Rome by Federigo Enriques to give several lectures on the recent advances in…
Lectures given at the Isaac Newton Institute, NATO-ASI School on "Confinement, Duality and Non-Perturbative Aspects of QCD", 23 June - 4 July, 1997.
I present a selection of conceptual and mathematical problems in the foundations of modern physics as they derive from the title question. Contribution to a panel session, "Springer Forum: Quantum Structures -- Physical, Mathematical and…
These notes are a summary of lectures given at the Instituto de Astronomia of the Universidad Nacional Autonoma de Mexico (UNAM), the Dipartimento di Fisica of the Universita degli studi di Salerno (Italy), and the Instituto de Fisica…
In these lectures several aspects of anyon in one and two dimensions are considered from the path integral formalism. This paper is based in a set of four lectures given by the author in the "V Latinoamerican Workshop of Particles and…
This essay is based on a physics lecture given at the Hong Kong University of Science and Technology on May 24, 2006, Hong Kong. It has 5 sections and one page of references and suggested reading. The section titles are: 1. Origin of the…
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 these lecture notes, we provide an introduction to the moduli space of Riemann surfaces, a fundamental concept in the theories of 2D quantum gravity, topological string theory, and matrix models. We begin by reviewing some basic results…
PhD thesis TU-Vienna, May 1994. Table of Contents: 1. Introduction, 2. Poisson Structure Induced Two Dimensional Field Theories, 3. Models of Gravity in 1+1 Dimensions
Starting from the work of the author in 1990 with different collaborators, essential progress in 2d gravity theories has been made. Now all such theories (and not only certain special models) can be treated at the classical as well as at…
We clarify the relation between 2-form Einstein gravity and its topological version. The physical space of the topological version is contained in that of the Einstein gravity. Moreover a new vector field is introduced into 2-form Einstein…
A slightly extended version, with a footnote added on December 19, 1997, of a contributed Abstract to the Eight Marcel Grossmann Meeting, Jerusalem, June 1997.