Photons and nonstandard analysis

[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

 

[mathman]

I believe the answer is no. Try this:

https://en.wikipedia.org/wiki/Influence_of_non-standard_analysis

 

[phoenixthoth]

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

 

[Demystifier]

For instance, considering the mass of a photon to be infinitesimal.

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.

 

[mathman]

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

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

 

[Demystifier]

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

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.

 

[bhobba]

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

Not quite.

It is useful as one way of handling that maddening Dirac Delta Function
http://math.stackexchange.com/questions/977491/dirac-delta-definition-in-non-standard-analysis

Although it is usually done using distribution theory.

Thanks
Bill

 

[HomogenousCow]

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