Includes many explicit detailed supereld quantum calculations presented for
the first time in a book.
Presents well-known theories alongside novel information on supersymmetric
eld theory models
Concentrates on perturbative aspects of supereld theory models
This book presents the supereld description of various supersymmetric eld theory models in
three- and four-dimensional space-times. A mapping between supereld and component
formulations of supersymmetric eld theories is discussed. The author also describes the
methodology for calculating quantum corrections in these theories employing supergraph
formalism and functional methods, and illustrates these approaches with many detailed
examples of how such calculations are performed for various supereld models.
1st ed. 2021, VIII, 158 p. 23 illus.
Hardcover
ISBN 978-3-030-68135-7
Product category : Monograph
Series : Fundamental Theories of Physics
Physics : Elementary Particles, Quantum Field Theory
State of the art results on the domination game and its variants
A toolbox of proof techniques is provided for the reader to obtain results on
the domination game and its variants
Powerful proof methods such as the imagination strategy are presented
Continuation Principle is developed, providing a much-used monotonicity
property of the game domination number
This concise monograph present the complete history of the domination game and its variants
up to the most recent developments and will stimulate research on closely related topics,
establishing a key reference for future developments. The crux of the discussion surrounds
new methods and ideas that were developed within the theory, led by the imagination strategy,
the Continuation Principle, and the discharging method of Bujtas, to prove results about
domination game invariants. A toolbox of proof techniques is provided for the reader to obtain
results on the domination game and its variants. Powerful proof methods such as the
imagination strategy are presented. The Continuation Principle is developed, which provides a
much-used monotonicity property of the game domination number. In addition, the reader is
exposed to the discharging method of Bujtas. The power of this method was shown by
improving the known upper bound, in terms of a graph's order, on the (ordinary) domination
number of graphs with minimum degree between 5 and 50.The book is intended primarily for
students in graph theory as well as established graph theorists and it can be enjoyed by
anyone with a modicum of mathematical maturity. The authors include exact results for several
families of graphs, present what is known about the domination game played on subgraphs
and trees, and provide the reader with the computational complexity aspects of domination
games. Versions of the games which involve only the “slow” player yield the Grundy domination
numbers, which connect the topic of the book with some concepts from linear algebra such as
zero-forcing sets and minimum rank. More than a dozen other related games on graphs and
hypergraphs are presented in the book.
Due 2021-04-27
1st ed. 2021, XIV, 130 p. 24 illus.
Softcover
ISBN 978-3-030-69086-1
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Graph Theory
Discusses major topics on Lie algebra and representation theory
Presents an accessible introduction to the major theorems of modern algebra
Provides a clear and motivating exposition with numerous examples and
exercises
Is written by an expert with over 43 years of teaching experience of the
subject
This book, the fourth book in the four-volume series in algebra, discusses Lie algebra and
representation theory in detail. It covers topics such as semisimple Lie algebras, root systems,
representation theory of Lie algebra, Chevalley groups and representation theory of Chevalley
groups.Numerous motivating illustrations have been presented along with exercises, enabling
readers to acquire a good understanding of topics which they can then use to find the exact or
most realistic solutions to their problems.
Due 2021-05-04
1st ed. 2021, IX, 346 p.
Hardcover
ISBN 978-981-16-0474-4
Product category : Graduate/advanced undergraduate textbook
Series : Infosys Science Foundation Series in Mathematical Sciences
Mathematics : Algebra
The main theme of our book is the very hot issue known as the Yau-TianDonaldson conjecture
As to the Yau-Tian-Donaldson conjecture, we focus on the open case on the
existence of extremal Kahler metrics
In our approach to the existence problem of extremal metrics, we use the
Chow norm very effectively
The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved
affirmatively by Chen-Donaldson-Sun and Tian. However, this conjecture is still open for general
polarizations or more generally in extremal Kahler cases. In this book, the unsolved cases of
the conjecture will be discussed. It will be shown that the problem is closely related to the
geometry of moduli spaces of test configurations for polarized algebraic manifolds. Another
important tool in our approach is the Chow norm introduced by Zhang. This is closely related
to Ding’s functional, and plays a crucial role in our differential geometric study of stability. By
discussing the Chow norm from various points of view, we shall make a systematic study of
the existence problem of extremal Kahler metrics.
Due 2021-04-24
1st ed. 2021, X, 128 p. 44 illus.
Softcover
ISBN 978-981-16-0499-7
Product category : Brief
Series : SpringerBriefs in Mathematics
Mathematics : Differential Geometry
Focuses on the life and works of the mathematical genius Srinivasa
Ramanujan
Discusses the role of Hardy and Chandrasekhar in Ramanujan’s life
Presents details on the busts and the life-size bronze statue of Ramanujan
Lists Ramanujan’s collected papers
Reviews his original notebooks and the “Lost Notebook”
This book offers a unique account on the life and works of Srinivasa Ramanujan?often hailed
as the greatest “natural” mathematical genius. Sharing valuable insights into the many stages
of Ramanujan’s life, this book provides glimpses into his prolific research on highly composite
numbers, partitions, continued fractions, mock theta functions, arithmetic, and hypergeometric
functions which led the author to discover a new summation theorem. It also includes the list
of Ramanujan’s collected papers, letters and other material present at the Wren Library of
Trinity College, Dublin, Ireland. This book is a valuable resource for all readers interested in
Ramanujan’s life, work and indelible contributions to mathematics.
Due 2021-05-14
1st ed. 2021, VIII, 252 p.
Hardcover
ISBN 978-981-16-0446-1
Product category : Biography
Mathematics : Number Theory
Pages: 352
ISBN: 978-981-122-997-8 (hardcover)
This book formulates a unified approach to the description of many-particle systems combining the methods of statistical physics and quantum field theory. The benefits of such an approach are in the description of phase transitions during the formation of new spatially inhomogeneous phases, as well in describing quasi-equilibrium systems with spatially inhomogeneous particle distributions (for example, self-gravitating systems) and metastable states.
The validity of the methods used in the statistical description of many-particle systems and models (theory of phase transitions included) is discussed and compared. The idea of using the quantum field theory approach and related topics (path integration, saddle-point and stationary-phase methods, Hubbard-Stratonovich transformation, mean-field theory, and functional integrals) is described in detail to facilitate further understanding and explore more applications.
To some extent, the book could be treated as a brief encyclopedia of methods applicable to the statistical description of spatially inhomogeneous equilibrium and metastable particle distributions. Additionally, the general approach is not only formulated, but also applied to solve various practically important problems (gravitating gas, Coulomb-like systems, dusty plasmas, thermodynamics of cellular structures, non-uniform dynamics of gravitating systems, etc.).
Preface
Introduction
Statistical Physics of Interacting Particle Systems
Statistical Description of Phase Transitions
Path Integration and Field Theory
Peculiarity of Calculation of Some Models
Statistical Description of Condensed Matter
Inhomogeneous Distribution in Systems of Particles
Cellular Structures in Condensed Matter
Statistical Description of Nonequilibrium Systems
Conclusions
Bibliography
Index
Graduate students and researchers interested in theoretical physics, condensed matter physics, astrophysics.
Pages: 500
ISBN: 978-981-123-189-6 (hardcover)
ISBN: 978-981-123-307-4 (softcover)
The book focuses on aspects of scientific truth that relate to our understanding of reality, and confronts whether truth is absolute or relative to what we are. Hence, it assesses the meaning of the scientific deductions we have made and how they have profoundly influenced our conception of life and existence.
The subtitle is 'From Wonder to Understanding', which is a paraphrased quote from Einstein, who said that the search for scientific truth is " ... a continual flight from wonder to understanding".
In addressing the goal of advancing our understanding of our place in the world, this book also reveals the development and details of diverse sciences, their connections and achievements, and that while perhaps the same fundamental questions exist, they are seen in the light of an ever-refined scientific perspective on reality.
Why the book is needed: many popular science books have been written, aimed at different levels of subject expertise, and nearly all treat their specific subject in isolation. Few attempt to link different sciences to their common foundations, and those that do are written by physicists. Since human knowledge is derived by, and relates to, the biological organism that human beings are, then such a book written from a biological perspective represents a novel perspective on the integration of science, and addresses new questions. This is such a book.
Impressive aspects: the depth, breadth, consistency, and clarity of the work.
Philosophy and Science
Physics and the Classical World
The Quantum World
The Biological World
The Evolving World
Consciousness and the World
Mind-Knowledge-Meaning
The educated/interested layperson, physicists, biologists, chemists, philosophers, and any scientist or philosopher interested in metaphysical problems, the connectivity of science, and subjects covered in the book.
Pages: 168
ISBN: 978-981-123-117-9 (hardcover)
ISBN: 978-981-123-283-1 (softcover)
Science has its roots in human curiosity. It is the process of exploration and research that has led to a better understanding of our surroundings: Copernicus set the Earth in its right place in our models of the Universe, Charles Darwin elucidated the mechanism of the evolution of living species, and Albert Einstein brought out the intimate connection between energy, space, and time.
This book provides a reliable guide to acquaint oneself with the scientific process. It explains in easy terms how scientific investigation has historically developed to reach our present understanding of the world around us. It also discusses the place of science in modern society in relation to culture and to the technological advances that it brings.
Foreword
Acknowledgments
Introduction
The Beginnings of Science
A Long Road
Toward the Infinitely Small
Toward the Infinitely Large
Our Origins
Science and Human Endeavor
Conclusion
Bibliography
Index
Educated lay readers interested in science and concerned about the current multipronged attack on science.