Why massless particle can only have two helicity states?

In summary: This applies to both QFT and other approaches, as for a massless particle it is not possible to define three perpendicular polarization vectors to the momentum vector. In summary, the symmetry reasons behind this are that the massless particle has the ability to drop four initial degrees of freedom to the two physical ones, while a massive particle can define three perpendicular polarization vectors. This was further discussed in the thread referenced above.
  • #1
liucl78
3
0
why massless particle, such as photon, can only have two helicity states?
Photon's helicity is 1,-1. Helicity zero is forbidden. why?
 
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  • #3
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 ([itex]A_{\mu}[/itex] 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...
 
  • #4
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...
 

1. Why can only massless particles have two helicity states?

According to the theory of relativity, massless particles travel at the speed of light and therefore do not experience time. This means they cannot have a rest frame and can only have two possible directions of spin, resulting in two helicity states.

2. What are the two possible helicity states of a massless particle?

The two helicity states are left-handed and right-handed spin. Left-handed spin particles spin in the opposite direction of their momentum, while right-handed spin particles spin in the same direction as their momentum.

3. How are helicity states related to chirality?

Helicity states and chirality are related, but not the same thing. Chirality refers to the asymmetry between left-handed and right-handed particles, while helicity states refer to the direction of spin of a particle. Massless particles can only have two helicity states, but they can have either left-handed or right-handed chirality.

4. Can massless particles change their helicity states?

No, massless particles cannot change their helicity states. This is because they travel at the speed of light and do not experience time, so they cannot rotate or change direction. Their helicity state is fixed and cannot be altered.

5. How does the number of helicity states affect the behavior of massless particles?

The number of helicity states affects how massless particles interact with each other and with other particles. For example, the weak nuclear force only affects left-handed particles, while the strong nuclear force only affects right-handed particles. This is due to the different interactions of the two helicity states with other particles.

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