规范场、扭结和引力

Preface

I Electromagnetism

1 Maxwell's Equations

2 Manifolds

3 Vector Fields

4 Differential Forms

5 Rewriting Maxwell's Equations

6 DeRham Theory in Electromagnetism Notes to Part I

II Gauge Fields

1 Symmetry

2 Bundles and Connections

3 Curvature and the Yang-Mills Equation

4 Chern-Simons Theory

5 Link Invariants from Gauge Theory Notes to Part II

III Gravity

1 Semi-Riemannian Geometry

2 Einstein's Equation

3 Lagrangians for General Relativity

4 The ADM Formalism

5 The New Variables

Notes to Part III

Index

is a book series polarized around the theory of knots. Volume 1 in the series is Louis H Kanffman's Knots and Physics.　　One purpose of this series is to continue the exploration of many of the themes indicated in Volume 1. These themes reach out beyond knot theory into physics, mathematics, logic, linguistics, philosophy, biology and practical experience. All of these outreaches have relations with knot theory when knot theory is regarded as a pivot or meeting place for apparently separate ideas. Knots act as such a pivotal place.We do not fully understand why this is so. The series represents stages in the exploration of this nexus.