Is Local the Same as Isotropic in Physics?

[Niles]

Hi

Say I have two expressions of the form

$$F(r, t) = \int{dr'\,dt'\,\,x(r,r',t,t')g(r',t')}$$

and

$$F'(r, t) = \int{dt'\,\,x'(r,t,t')g'(r, t')}$$

It is clear that F' is local in space, whereas F is non-local in space. Is it correct of me to say that F' describes an isotropic object? I.e., does isotropic = translational invariance?


Niles.

 

[mathman]

You should define the various symbols to make it a physics question. Right now they are mathematical expressions.

 

[Niles]

Good point, thanks. Say "x" denotes the susceptibility and "g" the electric field.

 

[mathman]

How about r, r', t, and t'.