using the to get a in the time term in a dot product (instead of using a metric tensor).

A Lorentz scalar Lagrangian density will be derived for each field theory we construct.
From the Lagrangian we can derive a field equation called the Euler-Lagrange equation.

The Lagrangian for a massive scalar field
can be deduced from the requirement that it be a scalar

where the last term is the interaction with a source. The Euler-Lagrange equation gives

which is the known as the

Using Fourier transforms, the field from a point source can be computed.

This is a field that falls off much faster than .

Jim Branson 2013-04-22