简介
This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.
目录
Preface
Electromagnetism p. 1
Maxwell's Equations p. 3
Manifolds p. 15
Vector Fields p. 23
Differential Forms p. 39
Rewriting Maxwell's Equations p. 69
DeRham Theory in Electromagnetism p. 103
Gauge Fields p. 159
Symmetry p. 161
Bundles and Connections p. 199
Curvature and the Yang-Mills Equation p. 243
Chern-Simons Theory p. 267
Link Invariants from Gauge Theory p. 291
Gravity p. 363
Semi-Riemannian Geometry p. 365
Einstein's Equation p. 387
Lagrangians for General Relativity p. 397
The ADM Formalism p. 413
The New Variables p. 437
Index p. 457
Electromagnetism p. 1
Maxwell's Equations p. 3
Manifolds p. 15
Vector Fields p. 23
Differential Forms p. 39
Rewriting Maxwell's Equations p. 69
DeRham Theory in Electromagnetism p. 103
Gauge Fields p. 159
Symmetry p. 161
Bundles and Connections p. 199
Curvature and the Yang-Mills Equation p. 243
Chern-Simons Theory p. 267
Link Invariants from Gauge Theory p. 291
Gravity p. 363
Semi-Riemannian Geometry p. 365
Einstein's Equation p. 387
Lagrangians for General Relativity p. 397
The ADM Formalism p. 413
The New Variables p. 437
Index p. 457
- 名称
- 类型
- 大小
光盘服务联系方式: 020-38250260 客服QQ：4006604884
云图客服：
用户发送的提问，这种方式就需要有位在线客服来回答用户的问题，这种 就属于对话式的,问题是这种提问是否需要用户登录才能提问
Video Player
×
Audio Player
×
pdf Player
×
