I have a question about the path integral formulation used in QED etc.
The path integral formulation implies to me that index of refraction (and reflection or anything also calculated using this formulation) are dependent on the macro geometry of the object. In the case of a refractive block of glass, the index of refraction should change based on the size of the block, and in the case of a mirror, the actual reflected image of my face would be different a 1m^2 mirror than it would be in a 10m^2 mirror... This is non-intuitive, as the phenomena is unobserved - My face looks the same in a 1m^2 mirror as it looks in a 10m^2 mirror...
Have I missed something? Or is it just that the coefficients in the integral have dropped off to such small numbers it makes no practical difference?
If that is the case, would an infinitely large mirror give a different looking reflection than a 1m^2 mirror? Would it stop reflecting or get better? The integral would be including infinitely many infinitely small terms... Would it slow light down to 0?