Metrics and forms

Tensors and Relativity: Chapter 3

Tensors in Special Relativity

We need to express the equations of physics in a frame independent way. This can be done for some equations by using four- vectors [ e.g. Newton's Laws  ] but what about the rest of physics!!?

We now extend this idea by introducing more general coordinate independent quantities called Tensors . In this section we will confine our discussion to Minkowski spacetime , although the concepts will apply to curved spacetime and General Relativity.

• Metrics and forms
• One- forms
• Gradients
• The metric as a mapping of vectors onto one- forms
• More general tensors
• Tensors of type 0/2
• Tensors of type 0/N
• Tensors of type 2/0
• Tensors of type M/0
• Tensors of type M/N
• Index ``raising'' and ``lowering''
• General properties of tensors
• Tensor derivatives and gradients
• Index
• About this document ...