# What is chirality?

I actually wanted to make the title as "What is the difference between chirality and helicity"? But I didn't do that because I don't understand properly what chirality is.

I have gone through this Wikipedia article: chirality to get the meaning of chirality? and what I get from there is that something is said to have chirality if it is not identical to its mirror image.

But I have often seen people saying a massless particle have same helicity (handedness, I think) and chirality? Now if the chirality has the above defination then how do people say it?

Again for massive particle we can have changed helicity by changing our reference frame. Ok I understand that, but How does it have anything to compare with chirality?

I have read these: Helicity and Chirality and many others in this site. But didn't find(or maybe didn't understand) the answer there which I am looking for.

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It would be easier if you told us your background. Do you know the Lorentz group, Dirac equation, special relativity... Do you understand that helicity is the projection of spin in the direction of momentum? – jinawee May 25 '14 at 20:05
@jinawee, I don't know group well,but know Lorentz transformation and all the other things that you have asked. – user22180 May 25 '14 at 20:56
@jinawee,As I don't know the group well, it may be one of the reason I am having the question. If this case can you please suggest some reference from where I can get some working knowledge of group to understand chirality. – user22180 May 25 '14 at 21:04
Here is a PDF comparing & contrasting the two concepts. This is part of a larger book that can be found here. – BMS May 25 '14 at 21:09

Chirality is a difficult phenomenon to wrap your head around, as it is a purely quantum mechanical phenomenon (like spin). It is closely related to helicity, but it is not the same (though it is equivalent for massless particles).

Chirality is a fundamental property of a particle; particles which differ in terms of chirality can be viewed as an entirely different type of particle. It refers to how a particle's quantum mechanical wave function behaves when a particle is rotated (or looked at from a different angle). For example, a spin 1/2 particle's wavefunction will gain a minus sign under a 360 degree rotation, as the rotation changes the complex phase of the wavefunction. The particle's chirality determines in a sense which way around the complex plain this phase travels to reach the -1, travelling in either a left handed way from 1 to -1, or a right handed way from 1 to -1.

The practical effect of this can be seen in how particles with different chiralities are treated by the weak interaction. Weak interactions will only affect left chiral particles not right chiral particles (and right chiral anti-particles, but not left anti-particles) i.e. the chirality of a particle has a measurable physical effect. A result of this is that neutrinos (which only interact via the weak interaction and gravity) are only observed in left chiral states. Sterile neutrinos, a hypothetical right chiral version of the neutrino, is a hot topic of current research, with some interesting hints having been seen (though they remain highly ambiguous, see http://resonaances.blogspot.co.uk/2012/02/other-neutrino-anomalies.html).

For an excellent exposition on chirality and helicity, see http://www.quantumdiaries.org/2011/06/19/helicity-chirality-mass-and-the-higgs/

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