Why massless particle can only have two helicity states?

Click For Summary

Discussion Overview

The discussion revolves around the question of why massless particles, specifically photons, can only exhibit two helicity states, with helicity zero being prohibited. The scope includes theoretical explanations from quantum field theory (QFT) and considerations of polarization vectors.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that the massless nature of particles like photons restricts them to two helicity states due to the properties of their fields in QFT.
  • One participant explains that in QFT, the degrees of freedom for a massless spin-1 particle can be reduced through gauge transformations, resulting in only two physical degrees of freedom.
  • Another participant adds that for massless particles, it is impossible to define three polarization vectors that are all perpendicular to the momentum vector, which contrasts with massive particles where two such vectors can always be found.
  • Some participants reference previous discussions and external links for further context on the topic.

Areas of Agreement / Disagreement

Participants present multiple viewpoints regarding the reasons behind the restriction of helicity states for massless particles, indicating that the discussion remains unresolved with competing explanations.

Contextual Notes

Limitations include the dependence on specific theoretical frameworks like QFT and the assumptions regarding the definitions of helicity and polarization vectors.

liucl78
Messages
3
Reaction score
0
why massless particle, such as photon, can only have two helicity states?
Photon's helicity is 1,-1. Helicity zero is forbidden. why?
 
Physics news on Phys.org
Because it's massless...
A massive spin1 particle introductively for QFT, can be studied in Proca's Lagrangian.

The symmetry reason is because of the possible unitary transformations you can have on your fields. These transformations (which will lead you in a specific gauge), such as the Lorentz gauge, will drop you initial degrees of freedom... In the photon's case, as massless, you have the abilitiy to do twice this trick, dropping the degrees of freedom 4 (A_{\mu} is a real 4 component field) to the physical degrees of freedom which is 2...
In other words you are killing components which can be "related" to the other components via a transformation, meaning they are not physical...
 
Apart from the QFT approach, the reason can go even further ahead. For example,for a massless particle you cannot really define 3 polarization vectors perpendicular to the momentum vector.
In the case of massive particle, in order to construct the polarization vectors, you can always find the 2 vectors with only spatial components which are perpendicular to the momentum vector... However for a massless particle, you cannot build a 3rd vector perpendicular to momentum ... it will be either longitudial or it will be a linear combination of the previous two...
 

Similar threads

Graduate Spin group for the Weyl equation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Spin and helicity conservation in QED
  • · Replies 3 ·
Replies
3
Views
6K
Undergrad Neutrino Helicity and Spin Uncertainty
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Helicity and electron/positron annihilation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Weyl Spinors & Helicity: Explained
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Questions about Helicity & Chirality: Answers Explained
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Polarization and helicity states
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Coleman: "Spin is a concept that applies only to particles with mass"
  • · Replies 11 ·
Replies
11
Views
2K
Graduate Helicity is different form Spin for massless particle(photon)?
  • · Replies 2 ·
Replies
2
Views
4K
Graduate Why are heilicty and chirality equivalent for massless particles?
  • · Replies 13 ·
Replies
13
Views
5K