Book Description
This book deals with the derivation of the Fokker-Planck equation, methods of solving it and some of its applications. Various methods such as the simulation method, the eigenfunction expansion, numerical integration, the variational method, and the matrix continued-fraction method are discussed. This is the first time that this last method, which is very effective in dealing with simple Fokker-Planck equations having two variables, appears in a textbook. The methods of solution are applied to the statistics of a simple laser model and to Brownian motion in potentials. It is shown that the solution of the equation for Brownian motion in a variety of potentials can be expressed in terms suitable for evaluation on a computer. A supplement is included, containing a short review of new material together with some recent references. The book should be very useful to graduate students in physics, chemical physics, and electrical engineering, and also to research workers in these fields.
Customer Reviews:
Rigorous book .......2006-12-28
This book is a classical reference in the subject of stochastic dynamics. It is a graduate level book written in clear and concise language. It covers all the basics about Langevin and Fokker-Planck equations (Chapters 3 and 4). In these chapters, Moyal expansion, Ito and Stratonovich interpretation of stochastic processes is presented carefully. Then they move on to study various methods of solving FP equation in the next 7 chapters. In the final chapter, FP equation and its application to Laser is discussed.
I recommend reading this book along with Gardiner's book (Handbook of Stochastic Methods) to anyone who wants to learn about stochastic dynamics seriously.
A good book on a difficult subject........2004-03-15
I got the impression that there are very few good textbooks on the subject of random processes in continuous time and the Fokker-Planck equation, which are accessible for physicists. In this book the subject presented in a manner that I thought to be a good compromise between mathematical rigor and physical intuition. For example to the spirit of the book, white noise is introduced both from the point of view of a physicist (it has a very short correlation time etc) and from the point of view of a mathematician (as the "derivative" of a Wiener process). While I found the book not very friendly or easy to read, it was one of my main sources for self-learning this subject during my Ph. D. work. I found the book three years ago, own it for two years and keep learning from it until today. I recommend the book very much.
Book Description
In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.
Customer Reviews:
Terrific geometry book for physicists.......2006-05-07
Advanced mathematics, such as differential geometry and topology, plays an important role in many areas of physics. This excellent book covers one of these topics, differential geometry. This is a topic essential for understanding general relativity and gauge theory. There are several good books aimed at physicists that cover differential geometry. While some of these have a broader scope than this book, nevertheless this book is my favorite one for differential geometry.
The topics covered include those necessary for reading advanced treatments of general relativity (such as Wald or Misner/Thorne/Wheeler). These include manifolds, fiber bundles, tangent/cotangent bundles, forms, Lie derivatives, Killing vectors and Lie groups.
Following this basic material a chapter covering some applications to physics, one example is electromagnetism. Up to this point the consideration of manifolds had been fairly general. In the final chapter the implications of adding a connection, and then a metric, are considered.
Why do I think this book is so good? It's not the breadth of material covered, this book is very focused on a limited range of material. It's the quality of the presentation for what it does cover. The development follows a logical order, the writing is exceptionally clear and the diagrams are very useful since Schutz explains them so well.
Integrability conditions discussed.......2004-01-21
Written in a attractive and even seductive way, relying more on Lie algebraic language than is typical, this book is probably as stimulating an intro. to modern geometry as you can find, within certain limits. The section on noncoordinate bases might have been more clearly written, however. Frobenius's theorm is discussed, something that Fomenko et al should have covered, and the section on connections can be worked throuigh independently of the heavy machinery of exterior differential forms, which is attractive for physics students.
Not as good as "a first course in general relativity".......2001-10-23
I had read first the "first course in general relativity"and was exited,so i fygured out that this book from the same author would reach the same standards,but it didnt.If Ihadnt read the first book from Schutz this book would be incomprenheceble.The greatest problem i think is the lack of exercices.Without them you cant really go anywhere.Another problem ,i believe,is the short space given to analyzeeach topic.Eventhough i understand tensor calculus very well I just cant get anywhere with the differential forms.
Eventhough its not the worst book out there its not the best either.My advise,buy a better book.
A Very Accessible Book ! Buy It !.......2000-11-06
This is a very enjoyable and clearly written book. From a physics point of view the approach is rather abstract, so although differential geometry is developed from 'scratch', it is probably better to have studied a more elementary text on the theory of 2-surfaces in 3-space first (eg Faber's book Differential Geometry and Relativity Theory ). The first chapter sets the mathematical background expected of the reader. The rudiments of analysis, topology, calculus of many variables and basic linear algebra is reviewed.The ensuing chapters cover differential geometry from a 'modern' viewpoint but the style is quite relaxed and the links to 'co-ordinate approach' are well explained. The exercises concentrate on the abstract approach. Throughout the book the underlying structure of manifolds is concentrated upon. No extra 'structure' eg connections and 'distance' concepts are added until the final chapter on Riemannian spaces. For example the metric tensor throughout the body of the book is merely used as a map between a tangent space and its dual space. It is only used as a 'distance' operator in the final chapter.For the purposes of independent study this is a sound book, there are hints and partial solutions for many of the exercises, which is always a welcome feature for those studying entirely on their own.
A Great Introduction to Diff. Geometry.......2000-08-08
This book presents the basic concepts of differential geometry in a clear, concise manner using modern notation. Schutz's writing style is very readable and there is a considerable breadth of coverage. In areas where one might wish for greater depth, Schutz provides excellent references. My only regret is that the physical applications chapters weren't longer. An excellent starter book and a good quick reference if you continue in differential geometry, GR or field theory.
Average customer rating:
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Applied Mathematical Methods in Theoretical Physics
Michio Masujima
Manufacturer: Wiley-VCH
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ASIN: 3527405348 |
Book Description
All there is to know about functional analysis, integral equations and calculus of variations in a single volume.
This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations.
After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory.
Throughout the book, the author presents over 150 problems and exercises - many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory—together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians.
Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.
Book Description
This book is aimed at those readers who already have some knowledge of mathematical methods and have also been introduced to the basic ideas of quantum optics. It should be attractive to students who have already explored one of the more introductory texts such as Loudon's The quantum theory of light (2/e, 1983, OUP) and are seeking to acquire the mathematical skills used in real problems. This book is not primarily about the physics of quantum optics but rather presents the mathematical methods widely used by workers in this field. There is no comparable book which covers either the range or the depth of mathematical techniques.
Customer Reviews:
Review of "Methods in theoretical quantum optics".......2001-10-18
I find this book really excellent. It gives a masterly
written introduction to all the most fundamental mathematical
methods in quantum optics. The concepts are introduced very
carefully, all the passages are explained in full detail, and
the discussion is very thorough throghout the book.
The authors gradually and clearly introduce the main
mathematical objects always relating them to basic
interactions and physical situations.
Special care is dedicated to the discussion of the basic
quantum states, number, thermal, coherent and squeezed.
Atomic coherent states and multimode extensions are discussed
as well. In each instance, simple Hamiltonian models
giving rise to the fundamental quantum states are
introduced and analysed in detail; among others,
I find excellent the detailed analysis devoted to the Jaynes--Cummings model, the beam splitter,
and the squeezing Hamiltonian.
Quite a substantial part of the book is dedicated
to the discussion of the statistical properties of the
electromagnetic field, in particular the
characteristic functions
and their associated quasiprobability distributions.
I believe that this book will be very useful both as
an introductory textbook for graduate and advanced
undergraduate students, as well as a reference book
for professionals working in the field of quantum optics
and basic quantum mechanics.
Average customer rating:
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Finite Element Methods for Maxwell's Equations (Numerical Analysis and Scientific Computation Series)
Peter Monk
Manufacturer: Oxford University Press, USA
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The Finite Element Method in Electromagnetics
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Inverse Acoustic and Electromagnetic Scattering Theory (Applied Mathematical Sciences)
ASIN: 0198508883 |
Book Description
Since the middle of the last century, computing power has increased sufficiently that the direct numerical approximation of Maxwell's equations is now an increasingly important tool in science and engineering. Parallel to the increasing use of numerical methods in computational electromagnetism there has also been considerable progress in the mathematical understanding of the properties of Maxwell's equations relevant to numerical analysis. The aim of this book is to provide an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains. Suitable variational formulations are developed and justified mathematically. An error analysis of edge finite element methods that are particularly well suited to Maxwell's equations is the main focus of the book. The methods are justified for Lipschitz polyhedral domains that can cause strong singularities in the solution. The book finishes with a short introduction to inverse problems in electromagnetism.
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Knots and Feynman Diagrams
Dirk Kreimer
Manufacturer: Cambridge University Press
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ASIN: 0521587611 |
Book Description
This volume explains how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. The author emphasizes how new discoveries in mathematics have inspired conventional calculational methods for perturbative quantum field theory to become more elegant and potentially more powerful methods. The material illustrates what may possibly be the most productive interface between mathematics and physics. As a result, it will be of interest to graduate students and researchers in theoretical and particle physics as well as mathematics.
Average customer rating:
- Fantastic - for the scientist
- a book worth keeping
- Phenomenal
- You should buy this, despite its flaws
- The perfect first book in differential geometry
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The Geometry of Physics: An Introduction
Theodore Frankel
Manufacturer: Cambridge University Press
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Geometry, Topology and Physics, Second Edition (Graduate Student Series in Physics)
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Advanced Calculus: A Differential Forms Approach
ASIN: 0521387531 |
Book Description
This book is intended to provide a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and engineering. Included are discussions of analytical and fluid dynamics, electromagnetism, thermodynamics, the deformation tensors of elasticity, soap films, special and general relativity, the Dirac operator and spinors, and gauge fields, including Yang-Mills, the Aharonov-Bohm effect, Berry phase, and instanton winding numbers. Before discussing abstract notions of differential geometry, geometric intuition is developed through a rather extensive introduction to the study of surfaces in ordinary space; consequently, the book should also be of interest to mathematics students. This book will be useful to graduate and advanced undergraduate students of physics, engineering and mathematics. It can be used as a course text or for self study.
Customer Reviews:
Fantastic - for the scientist.......2007-07-18
A very good book: buy it. But only if you are a scientist or student of physics/mathematics. This is not popular-science-common-public level.
a book worth keeping.......2007-05-01
This book can be quite confusing if you start without any background on the idea of manifold or knows nothing about general relativity. However, it does have strong points:
1. The notation is very up-to-date, and is entirely coordinate-independant approach.
2. The author explains in great details of formulation of modern differential geometry, and the details are comparatively lacking in other reference books.
3. The author never hesitate to use graphs and diagrams to illustrate points, and stroke nice balance in between mathematics rigor and physical insight.
Although it appears quite verbose at some point, it is mainly because differential geometry is such a heavy subject. Another book nice to have as companion reading is Goldburg's "Tensor analysis on Manifold", a terse, well-written text book.
Phenomenal .......2006-11-13
I just finished reading this book and I found it phenomenal. The physical ideas are made very clear in a natural mathematical framework.
You should buy this, despite its flaws.......2006-03-03
The other reviews on this page give this book anywhere from 1 to 5 stars, and they are all correct in their own way. The book is inspired, deep and full of physics applications and insights. On the other hand, it skims over mathematical rigor to a large degree and focuses more on defining things, getting a feel for them and moving on to application.
My advice: buy the book for its strengths, and read other books in parallel if you need more rigor. But still, buy it.
Also, things can be confusing on the first two or three reads, but keep at it and you will be glad you did.
The perfect first book in differential geometry.......2005-01-28
Differential geometry can be a very intimidating subject due to its heavy formalism. There are complete books (such as Kobayashi& Nomizu) very good as reference books, and there very few books that show the reader the picture behind the formulas.
This is one such book. It tells you the intuition behind each construction and from this point of view it has many things in common with Arnold's famous book on Math. Methods in Classical Mechanics. But where as Arnold does not pay too much attention to formalism, this book achieves this task as well. It shows the reader how to do those impossible computations as well.
This is definitely the first place to look at if you want to really learn differential geometry. If it seems difficult it is only because the subject is so.
Average customer rating:
- correction to dost
- Easy reading, complete proofs, plenty of exercises
- Don't waste your money
- MATH AND TOPOLOGY
- required reading for a topologist interested in physics
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Topology, Geometry, and Gauge Fields: Interactions (Applied Mathematical Sciences)
Gregory L. Naber
Manufacturer: Springer
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Rotations, Quaternions, and Double Groups
ASIN: 0387989471 |
Book Description
This book covers topology and geometry beginning with an accessible account of the extraordinary and rather mysterious impact of mathematical physics, especially gauge theory, on the study of the geometry and topology of manifolds. Much of the mathematics developed in the book to study the classical field theories of physics (de Rham cohomology, Chern classes, Semi-Riemannian manifolds, Cech cohomology, spinors etc.) is standard, but the treatment always keeps one eye on the physics and unhesitatingly sacrifices generality to clarity. The author brings the reader up to the level needed to conclude with a brief discussion of the Seiberg-Witten invariants. Although this volume can be read independently Naber carries on the program initiated in his earlier volume, Topology, Geometry and Gauge Fields: Foundations, Springer, 1997, and writes in much the same spirit with precisely the same philosophical motivation. A large number of exercises are included to encourage active participation on the part of the reader. This work will be of great interest to researchers and graduate students in the field of mathematical physics. REVIEWS OF TOPOLOGY, GEOMETRY, AND GAUGE FIELDS: FOUNDATIONS "It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics...Naber combines a knowledge of his subject with an excellent informal writing style." NZMS NEWSLETTER "...this book should be very interesting for mathematicians and
Customer Reviews:
correction to dost.......2006-05-20
The review "Easy reading, complete proofs, plenty of exercises, October 29, 2005 by Rehan Dost is of the first volume, Foundations, not this volume which is Interactions. Naber's books are crafted to bridge physics, undergraduate mathematics and graduate mathematics. This is one more of his beautiful volumes in applied mathematics.
Easy reading, complete proofs, plenty of exercises.......2005-10-30
This text is by far the best introductory text marrying basic concepts of physics with pure mathematics.
Some background in the basic concepts of vector calculus, linear algebra, complex numbers and group theory is required.
The author begins by motivating the mathematics by the pursuit of finding a vector potential to represent a magnetic monopole. We see that the topology of R3-0 precludes such a vector potential from existing. We see here a simple example of how the topology of a space affects the physics associated with it.
The importance of the vector potential as something other than a convenient computational tool is highlighted by a reference to essential inclusion in quantum mechanics. Thus we NEED such a potential.
The author now asks whether there is a "trick" or device to get around this difficulty. The device are principal bundles and connections. For example the potentials noted above must keep track of the phase of a charged test particle as it moves thru the field of a magnetic monopole. We need a "bundle" of circles ( representing the phase at each point ) over S2 ( the author explains why we need only consider S2 instead of R3-0, briefly we need only keep track of 2 of the 3 spherical co-ordinates ).
Thus a curve in S2 thought of as the particles trajectory will have to be "lifted" to the bundle space by a lifting procedure called a connection.
In a more general setting elementary particles have an internal structure ( spin etc ) which becomes apparent during interactions although may not be apparent in uniform motion thru a vacuum. Since the phase of the particle does not alter the modulus when calculating probabilities these do not change. However, when the particles interact phase differences are important. We need to keep track of such phases as the particles interact.
Thus we need a "bundle" over a 4-manifold ( keeps track of the particles space-time path ) to keep track of such internal states. One sees we also need a group to transform states into one another ( usually incorporated into the bundle ). Connections then model physical phenomena which mediate changes in the internal states.
We see that some connections satisfy the Yang-Mills equations and using the appropriate equivalence relation form Moduli spaces.
Now that may seem like alot to digest with only a spattering of mathematical maturity.
The beauty of the book is that the author starts from FIRST principles.
Chapter 1 introduces topological concepts of topology, continuity, quotient topology, projective spaces, compactness, connectivity, covering spaces and topological groups.
Chapter 2 introduces concepts of path lifting, fundamental groups, contractability, simple connectedness, covering homotopy theorem, higher homotopy groups
Chapter 3 introduces principle bundles, transition functions, bundle maps and principle bundles over spheres.
Chapter 4 introduces manifolds, derivatives on manifolds, tangent/cotangent spaces, submanifolds, vector fields, matrix lie groups, vector valued 1- forms, 2 forms and Riemann metrics
Chapter 5 gets to some physics with gauge fields and connections, curvature, Yang-Mills functional, moduli spaces, Hodge dual , matter fields and covariant derivatives.
At each step the author carefully provides complete proofs and easy exercises to ensure understanding.
It was a pleasure to read the book and complete the exercises. At no point did I feel frustration or boredom.
Don't waste your money.......2004-08-27
This review refers only to the book printing quality not to the contents.
I had purchased some books from Springer in the past (Like Arnold Mathematical Methods of Classical Mechanics, Lang Algebra etc..) and found them beautifully edited: good binding, paper etc..
And to my surprise I was very disappointed with the overall quality of this book, poor binding -glued instead of sewn- bad quality paper -forming waves at the binding spine, etc..
You pay for a quality item, a book you can use for years, and you get a hardbound crap that you can not left open in a table without holding it tight risking to lose the pages after a few days of use in the process.
I find this unacceptable in books costing 60$+. Sadly I find this to occur very often, publishers should be more careful with their printings and custumers should demand a better quality.
Don't waste your money.
A reader.
MATH AND TOPOLOGY.......2001-05-08
Topology is very important scince in the fields of mathematics. And it using in many of another sinceis.
required reading for a topologist interested in physics.......2000-05-14
As a mathematician turned physics grad student, it is often difficult to read "Math for Physicists" books simply because of the focus on making "numbers churn out;" which, at least for me personally, more difficult to get a handle on the subject and then, in turn, use it fruitfully.
This book on the other hand, is exemplary of why I got into physics in the first place. The first chapter (Physical motivations) and the last chapter (Gauge Fields and Instantons) can be read by any one with undergraduate topology under their belt and come away with a more powerful understanding of gauge theory than, in my opinion, can be found in other introductory gauge theory texts I've been directed to.
Of course I'll read all those said texts as well, but I'm thankful that I found this one.
Book Description
Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations. It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase. It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics). The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space. As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed. Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them.
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Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences (Springer Series in Synergetics)
An Introduction to Stochastic Processes in Physics (Johns Hopkins Paperback)
Nonequilibrium Statistical Mechanics
Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability)
Stochastic Processes in Physics and Chemistry, Third Edition (North-Holland Personal Library) (North-Holland Personal Library)
Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools (Springer Series in Synergetics)
Cybernetical Physics: From Control of Chaos to Quantum Control (Understanding Complex Systems)
Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments (Springer Series in Synergetics)
