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Why do QM particles with l<S vanish in a classical radiation field?

  1. Jan 29, 2010 #1
    Off pg 977 MTW Gravitation :

    Consider a classical radiation field whose associated quantum mechanical particles have integer spin S, and zero rest mass. Resolve that radiation field into spherical harmonics - i.e. into multipole moments. all components with l<S will vanish; in general those with l>=S will remain; and this is independent of the nature of the source!

    Can anyone reason me why l<S would vanish?
  2. jcsd
  3. Jan 30, 2010 #2
    The polarization or the multi pole moment of a radiation field is given by the number of degrees of freedom the field is capable of oscillating in. When the field is quantized the these degrees of freedom are identified with spin of the particle.

    The long ranged forces EM and gravitation are dipole and quadrapole respectively. Correspond to to the fact that they are mediated by photons(spin 1) and gravitons(spin 2) particles.
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