Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Why massless particle can only have two helicity states?

  1. Mar 21, 2014 #1
    why massless particle, such as photon, can only have two helicity states?
    Photon's helicity is 1,-1. Helicity zero is forbidden. why?
  2. jcsd
  3. Mar 21, 2014 #2

    Vanadium 50

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2017 Award

  4. Mar 21, 2014 #3


    User Avatar
    Gold Member

    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...
  5. Mar 21, 2014 #4


    User Avatar
    Gold Member

    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...
  6. Mar 21, 2014 #5


    User Avatar
    Science Advisor

    Find the complete answer in the following


Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook