Chirality/Helicity difference?

[qnach]

I think these two words is most often used in high-energy physics.
However, what are the differences between Chirality and Helicity

The clock always turns "clockwisely", if you look in front of the clock. Is that chirality or helicity?

 

[vanhees71]

Helicity is the projection of the total angular momentum of the particle to the direction of its momentum. Chirality is not so easy to understand. I have only a mathematical explanation for Dirac fermions, consisting of a lefthanded and a righthanded component. Chirality eigen spinors are eigenvectors of $\gamma_5=\mathrm{i} \gamma^0 \gamma^1 \gamma^2 \gamma^3$, and the projectors to left- and right-handed components are
$$P_{R/L}=\frac{1 \pm \gamma_5}{2}.$$
For massless Dirac fermions helicity and chirality eigenstates coincide, but not for massive ones.

 

[qnach]

Helicity is the projection of the total angular momentum of the particle to the direction of its momentum. Chirality is not so easy to understand. I have only a mathematical explanation for Dirac fermions, consisting of a lefthanded and a righthanded component. Chirality eigen spinors are eigenvectors of $\gamma_5=\mathrm{i} \gamma^0 \gamma^1 \gamma^2 \gamma^3$, and the projectors to left- and right-handed components are
$$P_{R/L}=\frac{1 \pm \gamma_5}{2}.$$
For massless Dirac fermions helicity and chirality eigenstates coincide, but not for massive ones.

The clock always turns "clockwisely", if you look in front of the clock. Is that chirality or helicity?

 

[strangerep]

The clock always turns "clockwisely", if you look in front of the clock. Is that chirality or helicity?

It's helicity, but the value depends on the relative momentum between you and the clock (i.e., whether you're approaching, or receding from, the clock).

Chirality has to do with whether a system is the same as its mirror image.

 

[vanhees71]

Hm, it's a bit difficult. On the one hand, I'd also say, it's helicity since the hands of the clock are rotating, but on the other hand, helicity is the projection of the angular momentum to the momentum of the particle, but if the particle (or here the clock) is at rest, I can't define helicity to begin with. So here it's chirality in a sense, because we define a direction out of the plane where the hands of the clock rotate and use our right hand to check whether it runs in positive (counter-clockwise) or negative (clockwise) direction.

In other words we need to compare the orientation of the hands' rotation with some (arbitrarily) fixed orientation, for which we practically use our right hand.

There is this funny tale about how to communicate with an alien, what's left and right, for which we have to use something generally available to define orientation. The best thing we have are neutrinos of the Standard Model, which always come as left-handed spinors (because they couple only via left-handed chiral interactions of quantum flavor dynamics). We also communicate that we always shake right hands to greet each other (supposed the aliens are similarly built as humans and thus have hands to shake). When the proud physicists meets the alien, it offers its left hand, because it's made of antimatter and thus calles the always right-handed antineutrinos "neutrinos" ;-)).

 

[strangerep]

On the one hand, I'd also say, it's helicity since the hands of the clock are rotating, but on the other hand, helicity is the projection of the angular momentum to the momentum of the particle, but if the particle (or here the clock) is at rest, I can't define helicity to begin with. So here it's chirality in a sense, because we define a direction out of the plane where the hands of the clock rotate and use our right hand to check whether it runs in positive (counter-clockwise) or negative (clockwise) direction.

But chirality is Lorentz-invariant, whereas helicity is not.

 

[vanhees71]

Helicity is Lorentz invariant for massless particles. That's while it's the natural choice for the polarization observables of massless particles/photons, while for massive particles spin is defined in its rest frame, which is a preferred frame for this case.

For the clock, it's clear that you can always choose the restframe of the clock to define the orientation.

 

[Meir Achuz]

If the alien offers his left hand, DON'T TOUCH IT!