This graduate level text describes in a unified fashion the statistical mechanics of random walks, random surfaces and random higher dimensional manifolds with an emphasis on the geometrical aspects of the theory and applications to the quantization of strings, gravity and topological field theory. With chapters on random walks, random surfaces, two-and higher-dimensional quantum gravity, topological quantum field theories and Monte Carlo simulations of random geometries, the text provides a self-contained account of quantum geometry from a statistical field theory point of view. The approach...

The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantization of geometrical objects. The majority of lectures at the Advanced Study Institute on Quantum Ge- ometry in Akureyri was on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary par- ticles and interactions. The geometric concept of one-dimensional extended objects, or strings, has always been at the core of superstring theory but...

This book begins with a description of continuum mechanics and a derivation of the linear equations for sound waves in fluids and elastic waves in solids. There is a brief chapter on the wave equations of electrodynamics. This is followed by a description of plane wave solutions and a discussion on concepts like reflection, refraction, polarization and the role of boundary conditions. The second part of the book deals with the development and application of distributions and Fourier transforms. Towards the end, dispersion, the method of stationary phase, Kramers-Kronig relations and various...

The fundamental structure of matter and spacetime at the shortest length scales remains an exciting frontier of basic research in theoretical physics. A unifying theme in this area is the quantization of geometrical objects. The majority of lectures at the Advanced Study Institute on Quantum Ge- ometry in Akureyri was on recent advances in superstring theory, which is the leading candidate for a unified description of all known elementary par- ticles and interactions. The geometric concept of one-dimensional extended objects, or strings, has always been at the core of superstring theory but...