Lie groups, physics, and geometry : : an introduction for physicists, engineers and chemists

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Lie groups, physics, and geometry : : an introduction for physicists, engineers and chemists / Robert Gilmore

資料種別:: 電子ブック
形態:: 1 online resource (xi, 319 p.)
著者名:: Gilmore, Robert
ISBN:: 9780511791390 [0511791399] (: electronic bk)
書誌ID:: EB00000237

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その他の標題:

Lie Groups, Physics, & Geometry

注記:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

主題:

Group theory; Lie groups

言語:

英語

目次情報:

Introduction / 1：

Lie groups / 2：

Matrix groups

Lie algebras / 4：

Matrix algebras / 5：

Operator algebras / 6：

Exponentiation / 7：

Structure theory for Lie algebras / 8：

Structure theory for simple Lie algebras / 9：

Root spaces and Dykin diagrams / 10：

Real forms / 11：

Riemannian symmetric spaces / 12：

Contraction / 13：

Hydrogenic atoms / 14：

Maxwell's equations / 15：

Lie groups and differential equations / 16：

References

Index

Preface

The program of Lie / 1.1：

A result of Galois / 1.2：

Group theory background / 1.3：

Approach to solving polynomial equations / 1.4：

Solution of the quadratic equation / 1.5：

Solution of the cubic equation / 1.6：

Solution of the quartic equation / 1.7：

The quintic cannot be solved / 1.8：

Example / 1.9：

Conclusion / 1.10：

Problems / 1.11：

Algebraic properties / 2.1：

Topological properties / 2.2：

Unification of algebra and topology / 2.3：

Unexpected simplification / 2.4：

Preliminaries / 2.5：

No constraints / 3.2：

Linear constraints / 3.3：

Bilinear and quadratic constraints / 3.4：

Multilinear constraints / 3.5：

Intersections of groups / 3.6：

Embedded groups / 3.7：

Modular groups / 3.8：

Why bother? / 3.9：

How to linearize a Lie group / 4.2：

Inversion of the linearization map: EXP / 4.3：

Properties of a Lie algebra / 4.4：

Structure constants / 4.5：

Regular representation / 4.6：

Structure of a Lie algebra / 4.7：

Inner product / 4.8：

Invariant metric and measure on a Lie group / 4.9：

Algebras of embedded groups / 4.10：

Basis vectors / 5.8：

Boson operator algebras / 5.10：

Fermion operator algebras / 6.2：

First order differential operator algebras / 6.3：

EXPonentiation / 6.4：

The covering problem / 7.1：

The isomorphism problem and the covering group / 7.3：

The parameterization problem and BCH formulas / 7.4：

EXPonentials and physics / 7.5：

Some standard forms for the regular representation / 7.6：

What these forms mean / 8.3：

How to make this decomposition / 8.4：

An example / 8.5：

Objectives of this program / 8.6：

Eigenoperator decomposition - secular equation / 9.2：

Rank / 9.3：

Invariant operators / 9.4：

Regular elements / 9.5：

Semisimple Lie algebras / 9.6：

Canonical commutation relations / 9.7：

Root spaces and Dynkin diagrams / 9.8：

Properties of roots / 10.1：

Root space diagrams / 10.2：

Dynkin diagrams / 10.3：

Compact and least compact real forms / 10.4：

Cartan's procedure for constructing real forms / 11.3：

Real forms of simple matrix Lie algebras / 11.4：

Results / 11.5：

Brief review / 11.6：

Globally symmetric spaces / 12.2：

Metric and measure / 12.3：

Applications and examples / 12.6：

Pseudo-Riemannian symmetric spaces / 12.7：

Inonu-Wigner contractions / 12.8：

Simple examples of Inonu-Wigner contractions / 13.3：

The contraction U(2) to H[subscript 4] / 13.4：

Two important principles of physics / 13.5：

The wave equations / 14.3：

Quantization conditions / 14.4：

Geometric symmetry SO(3) / 14.5：

Dynamical symmetry SO(4) / 14.6：

Relation with dynamics in four dimensions / 14.7：

DeSitter symmetry SO(4, 1) / 14.8：

Conformal symmetry SO(4, 2) / 14.9：

Spin angular momentum / 14.10：

Spectrum generating group / 14.11：

Maxwell's equations / 14.12：

Review of the inhomogeneous Lorentz group / 15.1：

Subgroups and their representations / 15.3：

Representations of the Poincare group / 15.4：

Transformation properties / 15.5：

The simplest case / 15.6：

First order equations / 16.2：

Additional insights / 16.3：

Bibliography / 16.5：

Introduction / 1：

Lie groups / 2：

Matrix groups

Lie algebras / 4：

Matrix algebras / 5：

Operator algebras / 6：

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