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  1. Why is only the left hand electron coupled to weak interaction?

  2. How can I tell the chirality of an electron?

Bruce Lee
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Xian-Hui
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  • see http://physics.stackexchange.com/questions/161170/how-can-we-measure-chirality-in-experiments – anna v Mar 03 '16 at 04:27
  • this is related http://www.nature.com/news/force-of-nature-gave-life-its-asymmetry-1.15995 – anna v Mar 03 '16 at 04:35

1 Answers1

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The chirality (left handedness/right handedness) of a fermion originates by the way it transforms under the appropriate representation of Lorentz algebra (in general the Poincare algebra). In this way, we can state that the left handed electron and the right handed electron are two fundamentally different entities (as they transform differently under the Lorentz algebra) coupled together by a Dirac mass term.

It has been observed that the left handed electron couples to a $SU(2)$ gauge field by experiments. Since the right handed electron is a different entity altogether, there is no reason that it should also transform similarly under the same gauge field. So there is no basically reason why the right handed electron should transform similarly under weak interaction.

The chirality of the electron can be easily told by a variety of examples. One of the simplest is colliding it with particles which also transform under weak interaction. The scattering cross sections if the electron is left handed or right handed in such a case will depend on its chirality and so you can easily tell them apart. Another way can be to determine its helicity, given you know the direction of its momentum.

Bruce Lee
  • 5,237
  • @Charlie i hope you got the point.. :) – Bruce Lee Mar 03 '16 at 07:48
  • As time goes on, the left hand elecrton will has right hand part due to the mass term, so , I used to thought that chirality belong only to the field, not the particle it born. because electron will always finally get both left and right hand part, so every electron in the world feels the weak interaction. You said that we can treat the left and right one as different particle ? can you be more specify about this, what about an electron has both part? Thanks . – Xian-Hui Mar 03 '16 at 09:09
  • @Charlie the Dirac spinor is composed of two fundamental irreducible representations, the left handed and the right handed representations, which transform differently under Lorentz transformations..therefore they are two fundamentally separate entities... – Bruce Lee Mar 03 '16 at 13:27