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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.
Historical surveys consider Judeo-Christian notions of space, Newtonian absolute space, perceptions from 18th century to the present, more. Numerous quotations and references. "Admirably compact and swiftly paced style." — Philosophy of Science.
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.
The proceedings of the first meeting on “New Worlds in Astroparticle Physics” focus on the joint field of particle physics and astrophysics. This is a field widely open to both theory and experiment. Important questions of particle physics — from the role of the Higgs scalar to the deconfined QCD phase, the developments beyond the Standard Model and the subtle behavior of neutrinos — are discussed. The same is true for the relevant questions in astrophysics and cosmology — from the fluctuations in the photon background radiation to large scale structure formation, dark matter searches and the origin of cosmic rays at very high energies. The two viewpoints, from the small sizes or from the large scales, are convergent and reveal the same universe: the universe of astroparticle physics.
Zeta-function regularization is a powerful method in perturbation theory, and this book is a comprehensive guide for the student of this subject. Everything is explained in detail, in particular the mathematical difficulties and tricky points, and several applications are given to show how the procedure works in practice, for example in the Casimir effect, gravity and string theory, high-temperature phase transition, topological symmetry breaking, and non-commutative spacetime. The formulae, some of which are new, can be directly applied in creating physically meaningful, accurate numerical calculations. The book acts both as a basic introduction and a collection of exercises for those who want to apply this regularization procedure in practice. Thoroughly revised, updated and expanded, this new edition includes novel, explicit formulas on the general quadratic, the Chowla-Selberg series case, an interplay with the Hadamard calculus, and also features a fresh chapter on recent cosmological applications, including the calculation of the vacuum energy fluctuations at large scale in braneworld and other models.
This volume is devoted mainly to one of the more relevant subjects of the last two decades, namely, Inhomogeneous Cosmological Models. This subject has undergone a remarkable advance during the last decade, and the achievements attained have been quite numerous both from the observational and the theoretical point of view.
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The strongest part of this volume is the treatment of nonperturbative field theory with implications for baryon number violation at high energies and cosmology. Also, the volume contains some fresh results concerning anyons, lattice field theory, perturbative field theory and astrophysics.
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