Bøger i Progress in Mathematical Physics serien

This eighteenth volume in the Poincare Seminar Series provides a thorough description of Information Theory and some of its most active areas, in particular, its relation to thermodynamics at the nanoscale and the Maxwell Demon, and the emergence of quantum computation and of its counterpart, quantum verification.

This book develops a novel approach to perturbative quantum field theory: starting with a perturbative formulation of classical field theory, quantization is achieved by means of deformation quantization of the underlying free theory and by applying the principle that as much of the classical structure as possible should be maintained.The resulting formulation of perturbative quantum field theory is a version of the Epstein-Glaser renormalization that is conceptually clear, mathematically rigorous and pragmatically useful for physicists. The connection to traditional formulations of perturbative quantum field theory is also elaborated on, and the formalism is illustrated in a wealth of examples and exercises.

This book deals with asymptotic solutions of linear and nonlinear equa­ tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp­ totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob­ lems of mathematical physics; certain specific formulas were obtained by differ­ ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter­ nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: "One can hope that in the near future a computational pro­ cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.

It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields.

The fourth one is devoted to Entropy, giving a comprehensive account of the history and various realizations of this concept, from thermodynamics to black holes, and includes theoretical and experimental discussions of the corresponding fluctuations for mesoscopic systems near equilibrium.

By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems.

It is meant, above all, for physicists who specialize in the field theory and physics of elementary particles and plasma, for mathe maticians dealing with nonlinear differential equations, differential geometry, and algebra, and the theory of Lie algebras and groups and their representa tions, and for students and post-graduates in these fields.

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity.

Includes examples of applications to physics. This title uses topological methods to analyze isotropic invariant manifolds in order to obtain asymptotic series of eigenvalues and eigenvectors for the multi-dimensional Schrodinger equation, and also takes into account the so-called tunnel effects. It reviews finite-dimensional linear theory.

This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view.

Presents a unified treatment of three important integrable problems relevant to both Celestial and Quantum Mechanics. This title is suitable for graduate students in mathematics and physics (including physical chemistry) and researchers concerned with the general areas of dynamical systems, statistical mechanics, and mathematical physics.

The aim of this book is to present the theory and applications of the relativistic Boltzmann equation in a self-contained manner, even for those readers who have no familiarity with special and general relativity.

Examines systems of linear PDEs with constant coefficients, focusing attention on null solutions of Dirac systems. This provides a different way to look at some important questions which arise when one tries to develop multi-dimensional theories.

Because of the correspondences existing among all levels of reality, truths pertaining to a lower level can be considered as symbols of truths at a higher level and can therefore be the "foundation" or support leading by analogy to a knowledge of the latter.

This book is the eighth in a series of Proceedings for the S eminaire Poincar e, which is directed towards a large audience of physicists and of mathematicians. This new volume of the Poincar e Seminar series "The Spin" corresponds to the eleventh such Seminar, held on December 8, 2007.

This book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation.It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method.Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.

The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics, geometry, particle physics, telecommunications, biology, ...

This book presents a Lagrangian approach model to formulate various fields of continuum physics, ranging from gradient continuum elasticity to relativistic gravito-electromagnetism. It extends the classical theories based on Riemann geometry to Riemann-Cartan geometry, and then describes non-homogeneous continuum and spacetime with torsion in Einstein-Cartan relativistic gravitation.It investigates two aspects of invariance of the Lagrangian: covariance of formulation following the method of Lovelock and Rund, and gauge invariance where the active diffeomorphism invariance is considered by using local Poincaré gauge theory according to the Utiyama method.Further, it develops various extensions of strain gradient continuum elasticity, relativistic gravitation and electromagnetism when the torsion field of the Riemann-Cartan continuum is not equal to zero. Lastly, it derives heterogeneous wave propagation equations within twisted and curved manifolds and proposes a relation between electromagnetic potential and torsion tensor.

This book on the theory of three-dimensional spinors and their applications fills an important gap in the literature. From the reviews:"Gathers much of what can be done with 3-D spinors in an easy-to-read, self-contained form designed for applications that will supplement many available spinor treatments.

Without using the customary Clifford algebras frequently studied in connection with therepresentations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature.

The spectral theory of linear operators plays a key role in the mathematical formulation of quantum theory. This textbook provides a concise and comprehensible introduction to the spectral theory of (unbounded) self-adjoint operators and its application in quantum dynamics. Many examples and exercises are included that focus on quantum mechanics.

Inspired by the Bourbaki seminar in mathematics in its organization, hence nicknamed "Bourbaphi", the Poincar e Seminar is held twice a year at the Institut Henri Poincar e in Paris, with cont- butions prepared in advance.

This book on the theory of three-dimensional spinors and their applications fills an important gap in the literature. From the reviews:"Gathers much of what can be done with 3-D spinors in an easy-to-read, self-contained form designed for applications that will supplement many available spinor treatments.

This enormous complex of theoreti cal and experimental efforts was the subject of the Fourth Workshop on Grand Unification held in Philadelphia and attended by over two hundred physicists. However, to display the logical scope of the workshop the proceedings are organized into five subject areas.

"Contains most of the invited papers of the Second Colloquium and Workshop on 'Random Fields: Rigorous Results in Statistical Mechanics' held in K'oszeg, Hungary between August 26 and September 1, 1984"--Pref.