ESI Lectures in Mathematics and Physics
ISBN print 978-3-03719-094-4,
DOI 10.4171/094
November 2019, 228 pages, softcover, 17 x 24 cm.
We focus on free fields and the corresponding quasi-free states and more precisely on Klein?Gordon fields and Dirac fields. The first chapters are devoted to preliminary material on CCR*-algebras, quasi-free states, wave equations on Lorentzian manifolds, microlocal analysis and to the important Hadamard condition, characterizing physically acceptable quantum states on curved spacetimes. In the later chapters more advanced tools of microlocal analysis, like the global pseudo-differential calculus on non-compact manifolds, are used to construct and study Hadamard states for Klein?Gordon fields by various methods, in particular by scattering theory and by Wick rotation arguments. In the last chapter the fermionic theory of free Dirac quantum fields on Lorentzian manifolds is described in some detail.
This monograph is addressed to both mathematicians and mathematical physicists. The first will be able to use it as a rigorous exposition of free quantum fields on curved spacetimes and as an introduction to some interesting and physically important problems arising in this domain. The second may find this text a useful introduction and motivation to the use of more advanced tools of microlocal analysis in this area of research.
Keywords: Quantum Field Theory, curved spacetimes, Hadamard states, microlocal analysis, pseudo-differential calculus
Zurich Lectures in Advanced Mathematics
ISBN print 978-3-03719-200-9
DOI 10.4171/200
December 2019, 737 pages, softcover, 17 x 24 cm.
The origins of dynamical systems trace back to flows and differential equations, and this is a modern text and reference on dynamical systems in which continuous-time dynamics is primary. It addresses needs unmet by modern books on dynamical systems, which largely focus on discrete time. Students have lacked a useful introduction to flows, and researchers have difficulty finding references to cite for core results in the theory of flows. Even when these are known substantial diligence and consultation with experts is often needed to find them.
This book presents the theory of flows from the topological, smooth, and measurable points of view. The first part introduces the general topological and ergodic theory of flows, and the second part presents the core theory of hyperbolic flows as well as a range of recent developments. Therefore, the book can be used both as a textbook ? for either courses or self-study ? and as a reference for students and researchers.
There are a number of new results in the book, and many more are hard to locate elsewhere, often having appeared only in the original research literature. This book makes them all easily accessible and does so in the context of a comprehensive and coherent presentation of the theory of hyperbolic flows.
Keywords: hyperbolic, hyperbolicity, flow, ergodic theory, topological dynamics, rigidity, expansiveness, shadowing, specification, geodesic flow, Anosov flow, Axiom A, entropy, equilibrium states, stable manifold, topological pressure, symbolic flows, Markov partitions
Due 2020-02-29
1st ed. 2019, Approx. 510 p.
Hardcover
ISBN 978-3-030-32795-8
This book aims to transfer geometric intuition to the algebraic framework of
Galois theory
Gives a parallel presentation of Galois theory and the theory of covering
spaces and highlights this similarity between the two
Useful both for undergraduates and graduates, as well as to any researcher
wishing to go beyond a purely algebraic approach to Galois theory.
Galois theory has such close analogies with the theory of coatings that algebraists use a
geometric language to speak of body extensions, while topologists speak of "Galois coatings".
This book endeavors to develop these theories in a parallel way, starting with that of coatings,
which better allows the reader to make images. The authors chose a plan that emphasizes this
parallelism. The intention is to allow to transfer to the algebraic framework of the Galois theory
the geometric intuition that one can have in the context of the coatings. This book is aimed at
graduate students and mathematicians curious about a non-exclusively algebraic view of Galois
theory.
Due 2020-01-23
1st ed. 2019, VIII, 142 p.
28 illus., 3 illus. in color.
Softcover
ISBN 978-3-030-33252-5
Quasi-One-Dimensional Approximation and General Formulation for
Subsonic, Transonic and Supersonic Flows
Offers a detailed explanation of the compressible flow theory, illustrated with
practical examples
Gathers together key information on compressible fluid flows, acoustic waves,
shock and numerical simulation applied to one- and multi-dimensional
problems
Presents a formal deduction of the nonlinear three-dimensional plus time
equation governing the velocity potential of irrotational and isentropic
compressible flow, not found in the standard literature
Uses modern, easily accessible language
This book offers a concise and practical survey of the principles governing compressible flows,
along with selected applications. It starts with derivation of the time-dependent, threedimensional
equation of compressible potential flows, and a study of weak waves, including
evaluation of the sound speed in gases. The following chapter addresses quasi-onedimensional
flows, the study of normal shock waves, and flow in ducts with constant cross
section subjected to friction and/or heat transfer. It also investigates the effects of friction and
heat transfer in ducts with variable cross section. The chapter ends by pointing to the analogy
between one-dimensional compressible flows and open channel hydraulics. Further, the book
discusses supersonic flows, including the study of oblique shock waves, and supersonic flows
over corners and wedges. It also examines Riemann problems, numerical resolution of the
wave equation, and of nonlinear hyperbolic problems, including propagation of strong waves. A
subsequent chapter focuses on the small perturbation theory of subsonic, transonic and
supersonic flows around slender bodies aligned or almost aligned to the uniform inflow. In
particular, it explores subsonic and supersonic flows over a wavy wall. Lastly, an appendix with
a short derivation of the Fluid Mechanics basic equations is included.
Due 2020-01-14
1st ed. 2019, X, 159 p. 65
illus., 50 illus. in color.
Hardcover
ISBN 978-3-030-32881-8
Presents structured regularizing preconditioners for image deblurring
Discusses applications in astronomical and medical imaging
Includes a chapter on variable metric first-order methods
This book presents recent mathematical methods in the area of inverse problems in imaging
with a particular focus on the computational aspects and applications. The formulation of
inverse problems in imaging requires accurate mathematical modeling in order to preserve the
significant features of the image. The book describes computational methods to efficiently
address these problems based on new optimization algorithms for smooth and nonsmooth
convex minimization, on the use of structured (numerical) linear algebra, and on multilevel
techniques. It also discusses various current and challenging applications in fields such as
astronomy, microscopy, and biomedical imaging. The book is intended for researchers and
advanced graduate students interested in inverse problems and imaging