Jerusalem Winter School For Theoretical Physics – serie

The subject of Quantum Cosmology is concerned with providing a quantum mechanical description of the universe as a whole and, within that description, to constructing a theory of the universe's initial condition whose predictions can be compared with observation. The recent progress in this area has profound implications for physics at all scales. The lectures at this School describe these theories and their implications. They cover basic quantum mechanics of cosmology, proposals for theories of initial conditions, and their application to the prediction of the large scale features of our universe. A special emphasis of the School is the implication of topological fluctuations of spacetime (wormholes, baby universes) for the observed coupling constants of the low energy interactions of elementary particles and as a potential explanation for the vanishing of the cosmological constant.

The subject of Quantum Cosmology is concerned with providing a quantum mechanical description of the universe as a whole and, within that description, to constructing a theory of the universe's initial condition whose predictions can be compared with observation. The recent progress in this area has profound implications for physics at all scales. The lectures at this School describe these theories and their implications. They cover basic quantum mechanics of cosmology, proposals for theories of initial conditions, and their application to the prediction of the large scale features of our universe. A special emphasis of the School is the implication of topological fluctuations of spacetime (wormholes, baby universes) for the observed coupling constants of the low energy interactions of elementary particles and as a potential explanation for the vanishing of the cosmological constant.

In the past few years there has been much study of random two dimensional surfaces. These provide simple models of string theories with a few degrees of freedom, as well as toy models of quantum gravity. They have possible applications to the statistical mechanics of phase boundaries and to the development of an effective string description of QCD.Recently, methods have been developed to treat these theories nonperturbatively, based on discrete triangulations of the surfaces that can be generated by simple matrix models. Exact solutions with a rich mathematical structure have emerged. All these matters are discussed fully in this book.

In the past few years there has been much study of random two dimensional surfaces. These provide simple models of string theories with a few degrees of freedom, as well as toy models of quantum gravity. They have possible applications to the statistical mechanics of phase boundaries and to the development of an effective string description of QCD.Recently, methods have been developed to treat these theories nonperturbatively, based on discrete triangulations of the surfaces that can be generated by simple matrix models. Exact solutions with a rich mathematical structure have emerged. All these matters are discussed fully in this book.

The study of the correlated motion of electrons in solids is of increasing importance in condensed matter physics. In the past few years, the discovery of high-temperature superconductors has stimulated an enormous theoretical effort in this area, building on earlier theories of heavy-fermion and organic superconductors, and magnetic insulators. In a separate development the discovery of the fractional quantum Hall effect stimulated research into the behavior of the two-dimensional electron gas in a strong transverse magnetic field.The lectures at this school gave a systematic presentation of the current status of the theory in these areas. They covered the fractional quantum Hall effect and the many-body physics of the Hubbard model and its extensions, paying particular attention to the properties of doped insulators which are relevant for high-temperature superconductivity. There were detailed discussions of situations for which controlled calculations may be carried out — specifically infinite dimensions, one dimension, and generalized models in which the fermions have N components and N → •.