非交换微分几何及其在物理学中的应用导论 英文版PDF电子书下载

1 Introduction 1

2 Differential Geometry 7

2.1 Differential manifolds 7

2.2 Metrics and connections 23

2.3 Cohomology 38

3 Matrix Geometry 45

3.1 Differential forms Ⅰ 46

3.2 Differential forms Ⅱ 65

3.3 Tensor products 74

3.4 Metrics 77

3.5 Yang-Mills connections 87

3.6 Linear connections 97

3.7 Curvature 109

4 Noncommutative Geometry 118

4.1 General algebras 118

4.2 Poisson structures 149

4.3 Topological algebras 155

4.4 Quantum groups 191

5 Vector Bundles 213

5.1 K-theory 213

5.2 A matrix analogue 228

5.3 Fredholm modules 231

6 Cyclic Homology 241

6.1 The universal calculus 241

6.2 Cyclic homology 250

6.3 Morita equivalence 255

6.4 The Loday-Quillen theorem 257

7 Modiflcations of Space-Time 260

7.1 Noncommutative space-time 261

7.2 A finite model 270

7.3 Fuzzy physics 280

8 Extensions of Space-Time 313

8.1 The spinning particle 313

8.2 Noncommutative electrodynamics 317

8.3 Modified Kaluza-Klein theory 325