Format: Paperback / softback, 305 pages, height x width: 235x155 mm, weight: 492 g, 21 Illustrations, color;
6 Illustrations, black and white; XIV, 305 p. 27 illus., 21 illus. in color
Series: Fundamental Theories of Physics 204
Pub. Date: 16-Mar-2023
ISBN-13: 9783030887834
Quantum theory is at the foundation of the physical description of our world. One of the people who contributed significantly to our conceptual understanding of this theory was Heinz-Dieter Zeh (1932-2018). He was the pioneer of the process of decoherence, through which the classical appearance of our world can be understood. This volume presents a collection of essays dedicated to his memory, written by distinguished scientists and scholars. They cover all aspects of the interpretation of quantum theory in general and the quantum-to-classical transition in particular. This volume provides illuminating reading to anyone seeking a deep understanding of quantum theory and its relevance to the foundations of physics.
Markus Arndt (Vienna)
Markus Aspelmeyer (Vienna)
Andrei Barvinsky (Moscow)
Dagmar Bruss (Dusseldorf)
Peter Byrne (writer, Everett biographer),
Lajos Diosi (Budapest)
Domenico Giulini (Hannover)
Klaus Hornberger (Duisburg-Essen)
Bei-Lok Hu (Maryland)
Alexander Kamenshchik (Bologna)
Heinrich Paes (Dortmund)
Maximilian Schlosshauer (Portland)
Ion-Olimpiu Stamatescu (Heidelberg),
Wojciech Zurek (Los Alamos).
Potentially 1-3 reprints of key papers by Dieter Zeh
Format: Paperback / softback, 838 pages, height x width: 235x155 mm, weight: 1288 g,
10 Illustrations, black and white; XVIII, 838 p. 10 illus
Series: Fundamental Theories of Physics 205
Pub. Date: 08-Apr-2023
ISBN-13: 9783030895914
This book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book.
Introduction.- Spacetime.- Galileian metric field.- Galileian
gravitational field.- Galileian electromagnetic field.- Joined spacetime
connection.- Classical dynamics.- Sources of gravitational and
electromagnetic fields.- Fundamental fields of phase space.- Geometric
structures of phase space.- Hamiltonian formalism.- Lie algebra of special
phase functions.- Classical symmetries.- Quantum bundle.- Galileian upper
quantum connection.- Quantum differentials.- Quantum dynamics.-
Hydrodynamical picture of QM.- Quantum symmetries.- Quantum differential
operators.- Quantum currents and expectation forms.- Sectional quantum
bundle.- Feynman path integral.- Conclusions and further developments.-
Examples.
Format: Paperback / softback, 486 pages, height x width: 235x155 mm, weight: 765 g, 9 Illustrations,
color; 12 Illustrations, black and white; XVII, 486 p. 21 illus., 9 illus. in color
Series: Fundamental Theories of Physics 206
Pub. Date: 04-Apr-2023
ISBN-13: 9789811681912
This book presents a comprehensive account of the renormalization-group (RG) method and its extension, the doublet scheme, in a geometrical point of view.
It extract long timescale macroscopic/mesoscopic dynamics from microscopic equations in an intuitively understandable way rather than in a mathematically rigorous manner and introduces readers to a mathematically elementary, but useful and widely applicable technique for analyzing asymptotic solutions in mathematical models of nature.
The book begins with the basic notion of the RG theory, including its connection with the separation of scales. Then it formulates the RG method as a construction method of envelopes of the naive perturbative solutions containing secular terms, and then demonstrates the formulation in various types of evolution equations. Lastly, it describes successful physical examples, such as stochastic and transport phenomena including second-order relativistic as well as nonrelativistic fluid dynamics with causality and transport phenomena in cold atoms, with extensive numerical expositions of transport coefficients and relaxation times.
Requiring only an undergraduate-level understanding of physics and mathematics, the book clearly describes the notions and mathematical techniques with a wealth of examples. It is a unique and can be enlightening resource for readers who feel mystified by renormalization theory in quantum field theory.
PART I Introduction to Renormalization Group (RG) Method
1 Introduction: Notion of Effective Theories in Physical Sciences
2 Divergence and Secular Term in the Perturbation Series of Ordinary Differential Equations
3 Traditional Resummation Methods
3.1 Reductive Perturbation Theory
3.2 Lindstedt's Method
3.3 Krylov-Bogoliubov-Mitropolsky's Method for Nonlinear Oscillators
4 Elementary Introduction of the RG method in Terms of the Notion of Envelopes
4.1 Notion of Envelopes of Family of Curves Adapted for a Geometrical Formulation of the RG Method
4.2 Elementary Examples: Damped Oscillator and Boundary-Layer Problem
5 General Formulation and Foundation of the RG Method: Ei-Fujii-Kunihiro
Formulation and Relation to Kuramoto's reduction scheme
6 Relation to the RG Theory in Quantum Field Theory
7 Resummation of the Perturbation Series in Quantum Methods
PART II Extraction of Slow Dynamics Described by Differential and Difference Equations
8 Illustrative Examples
8.1 Rayleigh/Van der Pol equation and jumping phenomena
8.2 Lotka-Volterra Equation
8.3 Lorents Model
9 Slow Dynamics Around Critical Point in Bifurcation Phenomena
10 Dynamical Reduction of A Generic Non-linear Evolution Equation with
Semi-simple Linear Operator11 A Generic Case when the Linear Operator Has a Jordan-cell Structure
12 Dynamical Reduction of Difference Equations (Maps)
13 Slow Dynamics in Some Partial Differential Equations
13.1 Dissipative One-Dimensional Hyperbolic Equation
13.2 Swift-Hohenberg Equation
13.3 Damped Kuramoto-Shivashinsky Equation
13.4 Diffusion in Porus Medium --- Barrenblatt Equation
14 Appendix: Some Mathematical Formulae
PART III Application to Extracting Slow Dynamics of Non-equilibrium
Phenomena
15 Dynamical Reduction of Kinetic Equations
15.1 Derivation of Boltzmann Equation from Liouville Equation
15.2 Derivation of the Fokker-Planck (FP) Equation from Langevin Equation
15.3 Adiabatic Elimination of Fast Variables in FP Equation: Derivation of Generalized Kramers Equations
16 Relativistic First-Order Fluid Dynamic Equation
17 Doublet Scheme and its Applications
17.1 General Formulation
17.2 Lorentz Model Revisited
18 Relativistic Causal Fluid dynamic Equation
19 Numerical Analysis of Transport Coefficients and Relaxation Times
20 Reactive-Multi-component Systems
21 Non-relativistic Case and Application to Cold Atoms
PART IV Summary and Future Prospect
Format: Paperback / softback, 365 pages, height x width: 235x155 mm, weight: 581 g, 5 Illustrations, color;
1 Illustrations, black and white; XII, 365 p. 6 illus., 5 illus. in color.
Pub. Date: 29-Jun-2023
ISBN-13: 9789811600197
This book contains an up-to-date survey and self-contained chapters on contact slant submanifolds and geometry, authored by internationally renowned researchers. The notion of slant submanifolds was introduced by Prof. B.Y. Chen in 1990, and A. Lotta extended this notion in the framework of contact geometry in 1996. Numerous differential geometers have since obtained interesting results on contact slant submanifolds.
The book gathers a wide range of topics such as warped product semi-slant submanifolds, slant submersions, semi-slant ?- -, hemi-slant ?- -Riemannian submersions, quasi hemi-slant submanifolds, slant submanifolds of metric f-manifolds, slant lightlike submanifolds, geometric inequalities for slant submanifolds, 3-slant submanifolds, and semi-slant submanifolds of almost paracontact manifolds. The book also includes interesting results on slant curves and magnetic curves, where the latter represents trajectories moving on a Riemannian manifold under the action of magnetic field. It presents detailed information on the most recent advances in the area, making it of much value to scientists, educators and graduate students.
General Properties of Slant Submanifolds in Contact Metric Manifolds.-
Curvature Inequalities for Slant Submanifolds in Pointwise Kenmotsu Space
Forms.- Some Basic Inequalities on Slant submanifolds in Space forms.-
Geometry of Warped Product Semi-Slant Submanifolds in Almost Contact Metric
Manifolds.- Slant and Semi Slant Submanifolds of Almost Contact and
Paracontact Metric Manifolds.- The Slant Submanifolds in the Setting of
Metric f-manifolds.- Slant, Semi-Slant and Pointwise Slant Submanifolds of
3-Structure Manifolds.- Slant Submanifolds of Conformal Sasakian Space
Forms.- Slant Curves and Magnetic Curves.- Contact Slant Geometry of
Submersions and Pointwise Slant and Semi-Slant Warped Product Submanifolds.
Format: Paperback / softback, 1012 pages, height x width: 235x155 mm, weight: 1590 g, 7 Illustrations,
color; 6 Illustrations, black and white; XV, 1012 p. 13 illus., 7 illus. in color. In 2 volumes, not available separately.
Series: Springer Texts in Statistics
Pub. Date: 25-Jun-2023
ISBN-13: 9783030705800
The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760.
1. The General Decision Problem.-
2. The Probability Background.-
3. Uniformly Most Powerful Tests.-
4. Unbiasedness: Theory and First Applications.-
5. Unbiasedness: Applications to Normal Distributions.-
6. Invariance.-
7. Linear Hypotheses.-
8. The Minimax Principle.-
9. Multiple Testing and Simultaneous Inference.-
10. Conditional Inference.-
11. Basic Large Sample Theory.-
12. Extensions of the CLT to Sums of Dependent Random Variables.-
13. Applications to Inference.-
14. Quadratic Mean Differentiable Families.-
15. Large Sample Optimality.-
16. Testing Goodness of Fit.-
17. Permutation and Randomization Tests.-
18. Bootstrap and Subsampling Methods.- A. Auxiliary Results.
Format: Hardback, 608 pages, height x width: 235x155 mm, 12 Illustrations, color;
6 Illustrations, black and white; XX, 608 p. 18 illus., 12 illus. in color.
Pub. Date: 15-Sep-2023
ISBN-13: 9783031319242
This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.
This volume consists of twelve chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I to III. Amongst the topics studied in this volume are the Nash blow up, the space of arcs in algebraic varieties, determinantal singularities, Lipschitz geometry, indices of vector fields and 1-forms, motivic characteristic classes, the Hilbert-Samuel multiplicity and comparison theorems that spring from the classical De Rham complex.
Singularities are ubiquitous in mathematics and science in general. Singularity theory is a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways.
The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook
1 Le Dung Trang and Bernard Teissier, Limits of tangents, Whitney
stratifications and a Plucker type formula.- 2 Anne Fruhbis-Kruger and
Matthias Zach, Determinantal singularities.- 3 Shihoko Ishii, Singularities,
the space of arcs and applications to birational geometry.- 4 Hussein
Mourtada, Jet schemes and their applications in singularities, toric
resolutions and integer partitions.- 5 Wolfgang Ebeling and Sabir M.
Gusein-Zade, Indices of vector fields and 1-forms.- 6 Shoji Yokura, Motivic
Hirzebruch class and related topics.- 7 Guillaume Valette, Regular vectors
and bi-Lipschitz trivial stratifications in o-minimal structures.- 8 Lev
Birbrair and Andrei Gabrielov, Lipschitz Geometry of Real Semialgebraic
Surfaces.- 9 Alexandre Fernandes and Jose Edson Sampaio, Bi-Lipschitz
invariance of the multiplicity.- 10 Lorenzo Fantini and Anne Pichon, On
Lipschitz Normally Embedded singularities.- 11 Ana Bravo and Santiago
Encinas, Hilbert-Samuel multiplicity and finite projections.- 12 Francisco J.
Castro-Jimenez, David Mond and Luis Narvaez-Macarro, Logarithmic Comparison
Theorems.
Format: Paperback / softback, 580 pages, height x width: 235x155 mm, weight: 902 g,
32 Illustrations, color; XVI, 580 p. 32 illus. in color.,
Series: Springer Series in Computational Mathematics 58
Pub. Date: 24-Jul-2023
ISBN-13: 9783031099533
Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.
Introduction.- Integration of Smooth Periodic Functions.- Constructions
of Lattice Rules.- Modified Construction Schemes.- Discrepancy of Lattice
Point Sets.- Extensible Lattice Point Sets.- Lattice Rules for Nonperiodic
Integrands.- Intrgration with Respect to Probability Measures.- Integration
of Analytic Functions.- Korobov's p-Sets.- Lattice Rules in the Randomized
Setting.- Stability of Lattice Rules.- L2-Approximation Using Lattice Rules.-
L -Approximation Using Lattice Rules.- Multiple Rank-1 Lattice Point Sets.-
Fast QMC Matrix-Vector Multiplication.- Partial Diffeential Equations With
Random Coefficients.- Numerical Experiments for Lattice Rule Construction
Algorithms.- References.- Index.