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Essential Textbooks in Physics

How to Derive a FormulaVolume 1: Basic Analytical Skills and Methods for Physical Scientistsby Alexei A Kornyshev & Dominic O’Lee (Imperial College London, UK)

Key Features: ○ This book emphasizes on skills,

tricks, approximations, testing and understanding results, learning through not only mathematical, but the vast number of physical examples

○ Engaging and exciting, the book is complemented with amusing statements and cartoons, historical anecdotes, and use of colour in insightful diagrams and plots

○ The book teaches in ‘interactive’ mode: some of the longer examples are cumulative case studies, demonstrating a set of methods in one go, which contain intermediate calculations as exercises

Readership: Advanced and enthusiastic school students preparing for universities, specializing in science; teachers and tutors; undergraduate students; university lecturers.

462pp Apr 2020978-1-78634-634-6 US$108 £95978-1-78634-644-5(pbk) US$58 £50

Infinite Dimensional and Finite Dimensional Stochastic Equations and Applications in Physicsedited by Wilfried Grecksch (Martin-Luther-University, Halle-Wittenberg, Germany) & Hannelore Lisei (Babeş-Bolyai University, Cluj-Napoca, Romania)

This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics. The topics presented in this volume are: dynamics of stochastic reaction-diffusion equations; stochastic Itô-Volterra backward equations in Banach spaces; stochastic equations of Schrö dinger type; optimal control of stochastic Navier-Stokes equations; quantum Hamilton equations from stochastic optimal control theory.

Readership: Graduate students and researchers in mathematics, physics, and science researchers interested in the physical applications of the theory of stochastic processes.

260pp Apr 2020978-981-120-978-9 US$98 £85

Reviews in Mathematical Physics

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Bestseller

A Guide to Mathematical Methods for PhysicistsAdvanced Topics and Applicationsby Michela Petrini (Sorbonne Université, Paris, France), Gianfranco Pradisi (University of Rome Tor Vergata, Italy) & Alberto Zaffaroni (University of Milano-Bicocca, Italy)

This book provides a self-contained and rigorous presentation of the main mathematical tools needed to approach many courses at the last year of undergraduate in Physics and MSc programs, from Electromagnetism to Quantum Mechanics. It complements A Guide to Mathematical Methods for Physicists with advanced topics and physical applications. The different arguments are organised in three main sections: Complex Analysis, Differential Equations and Hilbert Spaces, covering most of the standard mathematical method tools in modern physics.

One of the purposes of the book is to show how seemingly different mathematical tools like, for instance, Fourier transforms, eigenvalue problems, special functions and so on, are all deeply interconnected. It contains a large number of examples, problems and detailed solutions, emphasising the main purpose of relating concrete physical examples with more formal mathematical aspects.

Contents: Complex Analysis; Differential Equations; Hilbert Spaces; Appendices.

Readership: Students and professionals in the field.

308pp Oct 2018978-1-78634-548-6 US$88 £77978-1-78634-704-6(pbk) US$48 £40

Bestseller

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Infinite Dimensional Analysis, Quantum Probability and Related Topics

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New Titles! Notable Titles in Mathematical Physics

A Guide to Lie Systems with Compatible Geometric Structuresby Javier de Lucas (University of Warsaw, Poland) & Cristina Sardón Muñoz (Instituto de Ciencias Matemáticas, Spain)

The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.

Readership: The book is aimed at Physics and Mathematics students finishing their degree, doctoral students, and researchers.

424pp Feb 2020978-1-78634-697-1 US$148 £130

Homotopical Quantum Field Theoryby Donald Yau (The Ohio State University at Newark, USA)

This book provides a general and powerful definition of homotopy algebraic quantum field theory and homotopy prefactorization algebra using a new coend definition of the Boardman-Vogt construction for a colored operad. All of their homotopy coherent structures are explained in details, along with a comparison between the two approaches at the operad level. With chapters on basic category theory, trees, and operads, this book is self-contained and is accessible to graduate students.

Readership: Graduate students, mathematicians, mathematical physicists.

312pp Nov 2019978-981-121-285-7 US$118 £105

World Scientific Series on Nonlinear Science Series A - Volume 97

Toward General Theory of Differential-Operator and Kinetic Modelsby Nikolay Sidorov (Irkutsk State University, Russia), Denis Sidorov (Russian Academy of Sciences, Russia) & Alexander Sinitsyn(Universidad Nacional de Colombia, Bogotá, Colombia)

This volume provides a comprehensive introduction to the modern theory of differential-operator and kinetic models including Vlasov–Maxwell, Fredholm, Lyapunov–Schmidt branching equations to name a few. This book will bridge the gap in the considerable body of existing academic literature on the analytical methods used in studies of complex behavior of differential-operator equations and kinetic models. This monograph will be of interest to mathematicians, physicists and engineers interested in the theory of such non-standard systems.

Readership: Graduate students and researchers interested in mathematical physics, differential equations and mathematical modelling.

496pp Mar 2020978-981-121-374-8 US$148 £130

Series on Analysis, Applications and Computation - Volume 9

Nonlinear Waves A Geometrical Approachby Petar Popivanov (Bulgarian Academy of Sciences, Bulgaria) & Angela Slavova (Bulgarian Academy of Sciences, Bulgaria)

This volume provides an in-depth treatment of several equations and systems of mathematical physics, describing the propagation and interaction of nonlinear waves as different modifications of these: the KdV equation, Fornberg–Whitham equation, Vakhnenko equation, Camassa–Holm equation, several versions of the NLS equation, Kaup–Kupershmidt equation, Boussinesq paradigm, and Manakov system, amongst others, as well as symmetrizable quasilinear hyperbolic systems arising in fluid dynamics.

This volume is self-contained and equipped with simple proofs. It contains many exercises and examples arising from the applications in mechanics, physics, optics and, quantum mechanics.

Readership: University and graduate students, mathematicians, physicists, engineers and specialists in the fields of evolution PDEs and their applications.

208pp Nov 2018978-981-3271-60-9 US$88 £75

Chaos in Nature (2nd Edition)by Christophe Letellier (CORIA, Normandy University, France)

“This book is a delight to read. In part because of its historical sweep. It begins at the beginning of the main branches of Nature in which Chaos has been encountered and brings us up to date in a step by step, savant by savant description of the short steps forward, shorter steps backward, and sometimes giant steps forward, that have occurred. As we come to the present we encounter equations introduced to describe particular experiments or created to understand particular phenomena. We encounter the most significant constructions currently available for the description, possibly even the classification, of physical systems that may behave chaotically. Prof. Letellier at last points us in the direction of the future and shows us that there is no bridge to carry us from our present to this future ... Yet.” Foreword by Robert Gilmore

Readership: Advanced undergraduates and graduate students in nonlinear dynamics and chaos theory.

436pp Jun 2019978-981-120-119-6 US$148 £130

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Notable Titles in Mathematical Physics

Population Dynamics Algebraic and Probabilistic Approachby Utkir A Rozikov (V I Romanovskiy Institute of Mathematics, Uzbekistan)

A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.

The book presents algebraic and probabilistic approaches in the theory of population dynamics. It also includes several dynamical systems of biological models such as dynamics generated by Markov processes of cubic stochastic matrices; dynamics of sex-linked population; dynamical systems generated by a gonosomal evolution operator; dynamical system and an evolution algebra of mosquito population; and ocean ecosystems.

460pp Apr 2020978-981-121-122-5 US$148 £130

Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore - Volume 36

The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundlesedited by Richard Wentworth (University of Maryland, USA) & Graeme Wilkin (National University of Singapore, Singapore)

Key Features: ○ Contains a detailed introduction to Higgs

bundles and nonabelian Hodge theory○ An accessible introduction to algebraic stacks and the stack of Higgs

bundles○ Exciting new developments on spectral data and the link between

topological recursion and the quantization of Hitchin’s spectral curve

Readership: Graduate students and researchers interested in Higgs bundles and their interactions within different areas of mathematics and physics.

412pp Aug 2018978-981-3229-08-2 US$148 £130

Maxwell EquationInverse Scattering in Electromagnetismby Hiroshi Isozaki (University of Tsukuba, Japan)

This book leads the reader to the frontier of inverse scattering theory for electromagnetism. Beginning with elementary vector calculus, this book provides fundamental results for wave equations and Helmholtz equations, and summarizes the potential theory. It also explains the cohomology theory in an easy and straightforward way, which is an essential part of electromagnetism related to geometry. It then describes the scattering theory for the Maxwell equation by the time-dependent method and also by the stationary method in a concise, but almost self-contained manner. Based on these preliminary results, the book proceeds to inverse problem for Maxwell equation.

Readership: Undergraduates, graduate students, and researchers.

300pp Sep 2018978-981-3232-69-3 US$118 £104

Quantum Techniques in Stochastic Mechanicsby John Baez (UC Riverside & Centre for Quantum Technologies, Singapore) & Jacob D Biamonte (Skolkovo Institute of Science and Technology, Russia)

We introduce the theory of chemical reaction networks and their relation to stochastic Petri nets — important ways of modeling population biology and many other fields. We explain how techniques from quantum mechanics can be used to study these models. This relies on a profound and still mysterious analogy between quantum theory and probability theory, which we explore in detail. We also give a tour of key results concerning chemical reaction networks and Petri nets.

Readership: Graduate students and researchers in the field of quantum and mathematical physics.

276pp Feb 2018978-981-3226-93-7 US$98 £86

Ludwig Faddeev Memorial VolumeA Life in Mathematical Physicsedited by Mo-Lin Ge (Chern Institute of Mathematics, China), Antti J Niemi (Stockholm University, Sweden & UppsalaUniversity, Sweden), Kok Khoo Phua (NTU,Singapore) & Leon A Takhtajan (Stony Brook University, USA & Euler International Mathematical Institute, Russia)

Ludwig Faddeev is widely recognized as one of the titans of 20th century mathematical physics. His fundamental contributions to scattering theory, quantum gauge theories, and the theory of classical and quantum completely integrable systems played a key role in shaping modern mathematical physics. A gathering of contributions from some of the biggest names in mathematics and physics, this volume serves as a tribute to this legendary figure. Volume contributors include: Sir Michael Atiyah, Jürg Fröhlich, Roman Jackiw, Vladimir Korepin, Nikita Nekrasov, André Neveu, Alexander M Polyakov, Samson Shatashvili, Fedor Smirnov as well as Nobel laureates Frank Wilczek and C N Yang.

636pp Jul 2018978-981-3233-76-8 US$128 £113

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Bestsellers

Series on Knots and Everything - Volume 53

Knots and Physics (4th Edition)by Louis H Kauffman (University of Illinois, Chicago, USA)

“This book is an essential volume for the student of low-dimensional topology from which a serious student can learn most aspects of modern knot theory. Its informal tone encourages investigation on the part of the reader. The author leaves the reader items to puzzle out.” Mathematical Reviews

This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.

Readership: Physicists and mathematicians.

864pp Nov 2012978-981-4383-00-4 US$195 £162978-981-4383-01-1(pbk) US$92 £76

Differential Geometry for Physicists and Mathematicians  Moving Frames and DifferentialForms: From Euclid Past Riemannby José G Vargas (PST Associates, LLC, USA)

This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative — almost like a story being told — that does not impede sophistication and deep results.

Readership: Physicists and mathematicians working on differential geometry.

312pp Feb 2014978-981-4566-39-1 US$99 £82

Advanced Series in Mathematical Physics - Vol. 29

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras  (2nd Edition)By (author): Victor G Kac (MIT), Ashok K Raina(Tata Institute of Fundamental Research, India) & Natasha Rozhkovskaya (Kansas State University, USA)

The second edition of this book incorporates, as its first part, the largely unchanged text of the first edition, while its second part is the collection of lectures on vertex algebras, delivered by Professor Kac at the TIFR in January 2003. The basic idea of these lectures was to demonstrate how the key notions of the theory of vertex algebras — such as quantum fields, their normal ordered product and lambda-bracket, energy-momentum field and conformal weight, untwisted and twisted representations — simplify and clarify the constructions of the first edition of the book.

Readership: Mathematicians studying representation theory and theoretical physicists.

252pp Jul 2013978-981-4522-18-2 US$98 £81978-981-4522-19-9(pbk) US$38 £32

Quantum Field Theory and Its Macroscopic Manifestations Boson Condensation, Ordered Patterns and Topological Defectsby Massimo Blasone (Università di Salerno & INFN, Italy), Petr Jizba (Czech Technical University, Prague, Czech Republic) & Giuseppe Vitiello (Università di Salerno & INFN, Italy)“This book succeeds in helping the reader to understand how the macroscopic properties are generated out of quantum dynamics in the QFT framework. The level is adequate for graduate students with a basic knowledge of QFT.” Mathematical ReviewsReadership: Researchers in mathematical physics, theoretical physics, high energy physics, condensed matter physics and solid state physics. Advanced undergraduate and graduate students in physics.

544pp Feb 2011978-1-84816-280-8 US$159 £132978-1-911299-72-1(pbk) US$68 £56

Feynman Motivesby Matilde Marcolli (California Institute of Technology, USA)“This book is certainly a positive contribution to the field … it serves very well as a friendly introduction for those new to the field and as a useful and informative overview of the current state of affairs in this ever-burgeoning subject. In particular, some readers may find this book a useful primer for tackling the more detailed exposition of the top-down approach.” Mathematical ReviewsReadership: Graduate students and researchers in mathematical physics and theoretical physics.

236pp Jan 2010978-981-4271-20-2 US$48 £40978-981-4304-48-1(pbk) US$24 £20

In the Search for BeautyUnravelling Non-Euclidean Geometryby Voldemar Smilga“Thales, Pythagoras, Democritus, Plato, Aristotle, Omar Khayyam, St. Thomas d’Acquinas, Lobachevsky, Riemann and Einstein are just a few of the actors appearing in this engaging book. Smilga’s book is a pleasant read on the history of the struggle with Euclid’s fifth postulate, the emergence of non Euclidean geometry and its application in the theory of relativity. Highly recommended to anyone interested in the history of geometry and theory of relativity.” Seifallah Randjbar-Daemi, International Centre for Theoretical Physics (ICTP)Readership: All students, historians and researchers interested in mathematical physics.

248pp Jan 2019978-981-3274-35-8 US$78 £70 978-981-120-830-0(pbk) US$38 £35

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