Photons and nonstandard analysis

1. Sep 14, 2015

phoenixthoth

Hi PF contributors,

Have there been attempts to apply nonstandard analysis to the behavior of photons? For instance, considering the mass of a photon to be infinitesimal.

I'm guessing the answer is yes so if you could provide references, I would be much obliged.

phoenixthoth

2. Sep 14, 2015

mathman

3. Sep 14, 2015

phoenixthoth

Thanks for that. It looks like Brownian motion is the closest thing to an application of NSA to physics.

4. Sep 15, 2015

Demystifier

What is gained by considering the infinitesimal photon mass? Perhaps regularization of IR divergences? For that purpose, I guess the standard cutoff approach is much better, because it does not violate the gauge invariance.

Anyway, the cutoff is supposed to be "infinitely big", so it can be viewed as 1/infinitesimal, so it could also be treated by non-standard analysis.

5. Sep 15, 2015

mathman

In all my exposure to Brownian motion (mostly mathematical), NSA was never mentioned.

6. Sep 16, 2015

Demystifier

Anything that can be done by NSA, can also be done by more conventional limits. Moreover, in the technical sense the conventional methods are usually simpler. A possible advantage of NSA is a more intuitive picture, but intuition is a matter of practice.

7. Sep 16, 2015

Staff: Mentor

Last edited: Sep 16, 2015
8. Sep 17, 2015

HomogenousCow

Is there actually any merit to doing things with NSA? Does it make any calculations simpler?