Elementary Introduction to Quantum Geometry

1. Preliminary Material Part 1: the Path Integral. 2. The Free Relativistic particle. 3. One-Dimensional Quantum Gravity. 4. Branched Polymers. 5. Random Surfaces and Bosonic Strings. 6. Two-Dimensional Quantum Gravity. 7. The Fractal Structure of 2D Gravity. 8. The Causal Dynamical Triangulation model. Appendix A: Preliminary Material Part 2: Green Functions. Appendix B: Problem Sets 1-12. Appendix C: Solutions to Problem Sets 1-13.

Jan Ambjørn is a Danish physicist regarded as one of the founders of the statistical theory of geometries. The formalism has been applied to bosonic strings and to quantum gravity in two and higher dimensions, and it was developed as a tool to study string theory and quantum gravity non-perturbatively. A later development, especially designed to study quantum gravity, is known as Causal Dynamical Triangulation Theory. During his career Ambjørn has done research in numerous other areas, including quantum field theory and QCD, lattice gauge theories, the baryon asymmetry of the universe, matrix models, non-commutative field theory, string theory as well as the statistical theories of random paths and random surfaces. He is currently professor at the Niels Bohr Institute, Copenhagen and Radboud University, Nijmegen.