Understanding the Meaning and Definition of Green's Tensor

[Mapes]

In my little area of recent research, the Green's tensor is the relationship between a point force and the resulting displacement field for an infinite or semi-infinite region. However, I occasionally see other references to the Green's tensor in the elasticity and physics literature, and I'm not sure whether it has a similar meaning there. So: what does the Green's tensor mean to you, and is there a useful all-encompassing definition?

 

[pam]

I have seen the term "Greens function" used more commonly. The GF can sometimes be a tensor, which is probably where you saw that used.
It got its name because its first application was by the amateur mathematician Green.
It is enormously useful. You could find more about it in many advancedltextbooks in math physics or EM.
As a brief general definition, try:
$$\phi({\bf r})=\int G({\bf r},{\bf r'})\rho([\bf r'})d^3 r'$$
as the solution to Posisson's equation.

 

[SeniorTotor]

Dear Mapes,

Don't be impressed or puzzled by this terminology. Basically speaking, a Green function / propagator is merely the solution of a (partial) differential equation with a delta-function right hand side (the source). It is useful to get the PDE solution with more complex source (delta-function is not physical, but this is a useful trick), and usually there is a convolution somewhere (hence your word tensor). I hope it helps a little.