Bill_K

The Absolute Derivative

In relativity we typically deal with two types of quantities - fields, which are defined everywhere - and particle properties, which are defined only along a curve or world line. The familiar covariant derivative is appropriate when we need to differentiate a field. A field is a function of all four coordinates, and the covariant derivative of φ(x) consists of the four partial derivatives ∂φ/∂x^µ plus correction terms involving the Christoffel symbols, one for...