Effects of photons having a finite mass

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SUMMARY

The discussion centers on the implications of photons possessing a finite mass on the Coulomb potential between stationary charges. It is established that if photons were massive, the interaction would not result in a strictly zero potential at large distances; instead, it would yield a Yukawa potential, which decreases exponentially but never reaches zero. This concept is crucial in understanding the behavior of fundamental forces, particularly in particle physics, where massive exchange particles influence interactions.

PREREQUISITES
  • Understanding of Coulomb potential and electromagnetic interactions
  • Basic knowledge of particle physics concepts
  • Familiarity with Yukawa potential and its implications
  • Concept of exchange particles in force mediation
NEXT STEPS
  • Study the properties of Yukawa potential in particle physics
  • Learn about the role of exchange particles in fundamental forces
  • Explore the implications of massive versus massless particles in quantum field theory
  • Investigate the relationship between charge shielding and potential interactions
USEFUL FOR

Students of physics, particularly those interested in particle physics and electromagnetic theory, as well as researchers exploring fundamental forces and their interactions.

Saptarshi Sarkar
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TL;DR
Effect on Coulomb potential due to finite mass of photons
Few days back, our college professor told us that if a photon were to have a finite mass, then the Coulomb potential between two stationary charges separated by a distance r would be strictly zero beyond some distance.

He told us that it was due to the reason that photon is the elementary particle which is the reason behind Coulomb force. I didn't understand what he really meant as we haven't yet had the course on particle physics. Can anyone please explain it or refer to something that I can read?
 
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Saptarshi Sarkar said:
then the Coulomb potential between two stationary charges separated by a distance r would be strictly zero beyond some distance.
That is not true. With a massive exchange particle you get a Yukawa potential. For large distances it is decreasing (approximately) exponentially, it quickly gets irrelevant, but never zero. The strong interaction has such a potential, and it can also arise in some cases from the electromagnetic interaction if additional particles shield a point charge.
 
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