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In QFT, photons are vibrations in the electromagnetic field and matter is also vibrations in many fields. These vibrations result in things that behave in completely different ways. How does QFT explain this difference in behavior?

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    $\begingroup$ Hint: consider the spin of the field quanta. $\endgroup$ Oct 2 '16 at 14:15
  • $\begingroup$ Also their mass. $\endgroup$ Oct 2 '16 at 14:33
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“Ordinary matter” are fermions, spin-1/2 particles. These obey the Pauli exclusion principle and are represented as anti-commuting operators in QFT. Due to the spin, they are actually 4-spinors which are 4-component vectors which certain transformation properties under Lorentz transformations.

Also the fermions can have additional properties:

  • electric charge
  • color charge
  • weak isospin

Light is always massless, has no electric and no color charge. It is a spin-1 particle and does not have isospin.

If you take for instance the proton and neutrons, you find that they have

  • spin 1/2
  • electric charge $+1$ and $0$
  • no color charge
  • weak isospin $I_z = \pm 1/2$
  • Mass of around 1 GeV

If you take a look at elementary quarks, they also have the same spin. Their charges are $2/3$ and $-1/3$, they do have a (fundamental) color charge, also weak isospin and a much lighter mass (which depends on the renormalization scale).

In the framework of QFT, there are a lot of differences between fermions (“ordinary matter”) and light.

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