Lie Groups, Physics, and Geometry : An Introduction for Physicists, Engineers and Chemists - No Information Available

Instant online reading.
Don't wait for delivery!

Lie Groups, Physics, and Geometry

An Introduction for Physicists, Engineers and Chemists

By: No Information Available

Write A Review

Hardcover | 17 January 2008

At a Glance

Hardcover
332 Pages

Dimensions(cm)
24.41 x 16.99 x 1.91

Hardcover

RRP $157.95

$141.75

10%OFF

or 4 interest-free payments of $35.44 with

Ships in 5 to 7 business days

Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.

Industry Reviews

"Gilmore (physics, Drexel U.) takes an applications-base approach to Lie group theory as it relates to certain branches of applied mathematics and the physical sciences, basically distilling what he considers the most useful material of his much longer book (New York: Wiley, 1974). He begins with a discussion of Lie group theory's intellectual underpinnings in Galois theory and concludes with a chapter on the application of Lie group theory to solving differential equations, both subjects that are relatively rare in texts on Lie group theory. In between he offers chapters on matrix groups, Lie algebras, matrix algebras, operator algebras, EXPonentiation, structure theory for Lie algebras, root spaces and Dynkin diagrams, real forms, Riemannian symmetric spaces, contraction, hydrogenic atoms, and Maxwell's equations." Book News Inc.

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Algebra Groups & Group Theory Applied Mathematics Engineering & Technology Technology in General Maths for Engineers Engineering in General Science Physics

Preface	p. xi
Introduction	p. 1
The program of Lie	p. 1
A result of Galois	p. 2
Group theory background	p. 3
Approach to solving polynomial equations	p. 8
Solution of the quadratic equation	p. 10
Solution of the cubic equation	p. 11
Solution of the quartic equation	p. 15
The quintic cannot be solved	p. 17
Example	p. 18
Conclusion	p. 21
Problems	p. 22
Lie groups	p. 24
Algebraic properties	p. 24
Topological properties	p. 25
Unification of algebra and topology	p. 27
Unexpected simplification	p. 29
Conclusion	p. 29
Problems	p. 30
Matrix groups	p. 34
Preliminaries	p. 34
No constraints	p. 35
Linear constraints	p. 36
Bilinear and quadratic constraints	p. 39
Multilinear constraints	p. 42
Intersections of groups	p. 43
Embedded groups	p. 43
Modular groups	p. 44
Conclusion	p. 46
Problems	p. 47
Lie algebras	p. 55
Why bother?	p. 55
How to linearize a Lie group	p. 56
Inversion of the linearization map: EXP	p. 57
Properties of a Lie algebra	p. 59
Structure constants	p. 61
Regular representation	p. 62
Structure of a Lie algebra	p. 63
Inner product	p. 64
Invariant metric and measure on a Lie group	p. 66
Conclusion	p. 69
Problems	p. 69
Matrix algebras	p. 74
Preliminaries	p. 74
No constraints	p. 74
Linear constraints	p. 75
Bilinear and quadratic constraints	p. 78
Multilinear constraints	p. 80
Intersections of groups	p. 80
Algebras of embedded groups	p. 81
Modular groups	p. 81
Basis vectors	p. 81
Conclusion	p. 83
Problems	p. 83
Operator algebras	p. 88
Boson operator algebras	p. 88
Fermion operator algebras	p. 89
First order differential operator algebras	p. 90
Conclusion	p. 93
Problems	p. 93
EXPonentiation	p. 99
Preliminaries	p. 99
The covering problem	p. 100
The isomorphism problem and the covering group	p. 105
The parameterization problem and BCH formulas	p. 108
EXPonentials and physics	p. 114
Conclusion	p. 119
Problems	p. 120
Structure theory for Lie algebras	p. 129
Regular representation	p. 129
Some standard forms for the regular representation	p. 129
What these forms mean	p. 133
How to make this decomposition	p. 135
An example	p. 136
Conclusion	p. 136
Problems	p. 137
Structure theory for simple Lie algebras	p. 139
Objectives of this program	p. 139
Eigenoperator decomposition - secular equation	p. 140
Rank	p. 143
Invariant operators	p. 143
Regular elements	p. 146
Semisimple Lie algebras	p. 147
Canonical commutation relations	p. 151
Conclusion	p. 153
Problems	p. 154
Root spaces and Dynkin diagrams	p. 159
Properties of roots	p. 159
Root space diagrams	p. 160
Dynkin diagrams	p. 165
Conclusion	p. 168
Problems	p. 168
Real forms	p. 172
Preliminaries	p. 172
Compact and least compact real forms	p. 174
Cartan's procedure for constructing real forms	p. 176
Real forms of simple matrix Lie algebras	p. 177
Results	p. 181
Conclusion	p. 182
Problems	p. 183
Riemannian symmetric spaces	p. 189
Brief review	p. 189
Globally symmetric spaces	p. 190
Rank	p. 191
Riemannian symmetric spaces	p. 192
Metric and measure	p. 193
Applications and examples	p. 194
Pseudo-Riemannian symmetric spaces	p. 197
Conclusion	p. 198
Problems	p. 198
Contraction	p. 205
Preliminaries	p. 205
Inonu-Wigner contractions	p. 206
Simple examples of Inonu-Wigner contractions	p. 206
The contraction U(2) to H[subscript 4]	p. 211
Conclusion	p. 216
Problems	p. 217
Hydrogenic atoms	p. 221
Introduction	p. 221
Two important principles of physics	p. 222
The wave equations	p. 223
Quantization conditions	p. 224
Geometric symmetry SO(3)	p. 227
Dynamical symmetry SO(4)	p. 230
Relation with dynamics in four dimensions	p. 233
DeSitter symmetry SO(4, 1)	p. 235
Conformal symmetry SO(4, 2)	p. 238
Spin angular momentum	p. 243
Spectrum generating group	p. 245
Conclusion	p. 249
Problems	p. 250
Maxwell's equations	p. 259
Introduction	p. 259
Review of the inhomogeneous Lorentz group	p. 261
Subgroups and their representations	p. 262
Representations of the Poincare group	p. 264
Transformation properties	p. 270
Maxwell's equations	p. 273
Conclusion	p. 275
Problems	p. 275
Lie groups and differential equations	p. 284
The simplest case	p. 285
First order equations	p. 286
An example	p. 290
Additional insights	p. 295
Conclusion	p. 302
Problems	p. 303
Bibliography	p. 309
Index	p. 313
Table of Contents provided by Ingram. All Rights Reserved.

Lie Groups, Physics, and Geometry

An Introduction for Physicists, Engineers and Chemists

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Maths for Engineers

Modern Engineering Mathematics

6th Edition

Bird's Engineering Mathematics

9th Edition

Bird's Higher Engineering Mathematics

9th Edition

Mathematics for Technicians

7th Edition

Modern Engineering Mathematics pack with MyMathLab Global

6th edition

Mathematics for Machine Learning

Iterative Methods for Linear and Nonlinear Equations

Frontiers in Applied Mathematics

Essential Mathematical Skills

For Engineering, Science and Applied Mathematics : 2nd Edition

Multi-Attribute Decision-Making

Theory, Emerging Methods, and Applications

Introduction to Civil Engineering

A Guide for Students and Professionals

Applied Engineering Mathematics with MATLAB® and Python

From Theory to Practice

Fuzzy-Model-Based Mode Control of Complex Nonlinear Systems

Engineering Mathematics and Operations Research

Dynamic Characteristics of Layered Structures: Mathematical Modelling, and Numerical Simulations

Mathematical Modelling, and Numerical Simulations

Fuzzy Sets and Triangular Norms

Aggregation in Decision-Aided Intelligent Systems

An Engineering Approach to Asymptotics and Approximations

With Applications in Optical Wave Propagation and Imaging in Turbulence

ISE Numerical Methods for Engineers

8th edition

Mathematical Methods for Physics and Engineering

A Comprehensive Guide

Foundations of Mathematical Modeling and Analysis in Engineering

Engineering Mathematics with MATLAB Applications

Vol. 1, Fundamentals

Ergodic Theory

A Probabilistic Approach to Dynamical Systems

Theoretical Fluid Mechanics

An application-oriented introduction with detailed derivations

Mathematical Systems Theory III

Linear Quadratic Control and Adaptive Feedback

Concise Guide to Fault Tree Analysis

Models, Methods and Algorithms

Branch-and-Price

This product is categorised by