Classical Field Theory

On Electrodynamics, Non-Abelian Gauge Theories
and Gravitation

• Maxwell’s Equations
• Symmetries and Covariance of the Maxwell Equations
• Maxwell Theory as a Classical Field Theory .
• Simple Applications of Maxwell Theory
• Local Gauge Theories
• Classical Field Theory of Gravitation
  • Introduction
  • Phenomenology of Gravitational Interactions
    • Parameters and Orders of Magnitude
    • Equivalence Principle and Universality
    • Red Shift and Other Effects of Gravitation
    • Some Conjectures and FurtherProgram
  • Matter and Non gravitational Fields
  • Spacetimes as Smooth Manifolds
    • Manifolds,Curves,and Vector Fields
    • One-Forms,Tensors, and Tensor Fields
    • Coordinate Expressions and Tensor Calculus
  • Parallel Transport and Connection
    • Metric, Scalar Product, and Index
    • Connection and Covariant Derivative
    • Torsion and Curvature Tensor Fields
    • TheLevi-CivitaConnection
    • PropertiesoftheLevi-CivitaConnection
    • Geodesics on Semi-Riemannian Spacetimes
    • More Properties of the CurvatureTensor
  • The Einstein Equations
    • Energy-Momentum Tensor Field in Curved Spacetime
    • Ricci Tensor, Scalar Curvature, and Einstein Tensor .
    • The Basic Equations
  • Gravitational Field of a Spherically Symmetric Mass Distribution
    • The Schwarzschild Metric
    • Two Observable Effects
    • The Schwarzschild Radius is an Event Horizon
  • Some Concluding Remarks