Covariant classical field theory

Many important examples of classical field theories which are of interest in quantum field theory are given below. In particular, these are the theories which make up the Standard model of particle physics. These examples will be used in the discussion of the general mathematical formulation of classical field theory.

In order to formulate a classical field theory, the following structures are needed:

This completes the mathematical prerequisites for a large number of interesting theories, including those given in the examples section above.

In weak gravitational curvature, flat spacetime often serves as a good approximation to weakly curved spacetime. For experiment, this approximation is good. The Standard Model is defined on flat spacetime, and has produced the most accurate precision tests of physics to date.