The papers included here deal with the many faces of renormalization group formalism as it is used in different branches of theoretical physics. The subjects covered emphasize various applications to the theory of turbulence, chaos, quantum chaos in dynamical systems, spin systems and vector models. Also discussed are applications to related topics such as quantum field theory and chromodynamics, high temperature superconductivity and plasma physics.

CP violation is one of the most subtle effects in the Standard Model of particle physics and may be the first clue to the physics that lies beyond. Charge conjugation, C, and parity, P, are symmetries of particle interactions. C corresponds to the operation of replacing a particle by its antiparticle, while P is the operation of mirror reflection. Before 1956, it was believed that these were also symmetries of the interactions of elementary particles. In 1956, C S Wu found evidence for P violation in the weak interaction. Theorists proposed that the combination of CP would be a symmetry of the weak interaction. In 1964, Christenson, Cronin, Fitch and Turlay found the first evidence for the violation of CP symmetry in the decays of kaons.Although Kobayashi and Maskawa then showed how the Standard Model can accommodate the observed CP violation, Wolfenstein pointed out that it is also possible that there is a new interaction in addition to the usual four, called the superweak interaction, which is responsible for the asymmetry. To test this idea, the observation of a different type of asymmetry, called direct CP violation, is required; in the kaon sector, very precise measurements of the ratio of kaon decay rates are necessary. In B decay modes where a second order weak process whimisically named “penguin” interferes with another suppressed, first order “tree” amplitude, it may also be possible to observe these direct CP-violating effects.B physics and CP violation is now one of the major growth areas in high energy physics. Nearly every major high energy physics laboratory now has a project underway to observe the large CP asymmetries expected in the B sector and to test the consistency of the Standard Model. The unitarity of the Kobayashi-Maskawa mixing matrix in the Standard Model implies the existence of three phases, called alpha, beta and gamma, which can be determined by the measurements of CP asymmetries in B decays. About 200 participants gathered in Hawaii in March 1997 to discuss the progress in the field, and this important book constitutes the proceedings of that conference.

This volume covers the collective behaviour of the Standard Model at finite temperature and density. The main physics motivation for this research comes from the early history of the Universe and also from the experimental efforts to create the quark-gluon plasma in laboratory experiments. Advances in theoretical investigations (effective theories, progress in numerical simulations, etc.) as well as the phenomenological applications figure in the broad spectrum of invited lectures. Prospective studies of beyond-the-Standard-Model theories receive particular attention. Non-equilibrium phenomena, especially questions related to baryon generation due to the electroweak anomaly and inflationary dynamics, are also discussed.

The subject of the exact renormalization group started from pioneering work by Wegner and Houghton in the early seventies and, a decade later, by Polchinski, who formulated the Wilson renormalization group for field theory. In the past decade considerable progress has been made in this field, which includes the development of alternative formulations of the approach and of powerful techniques for solving the exact renormalization group equations, as well as widening of the scope of the exact renormalization group method to include fermions and gauge fields. In particular, two very recent results, namely the manifestly gauge-invariant formulation of the exact renormalization group equation and the proof of the c-theorem in four dimensions, are presented in this volume.