Chirality VS. Helicity | Spin and Lorentz Group

Chirality and helicity often appear at the same time in a lecture and often it’s difficult to figure out their difference. So what exactly is the difference between chirality and helicity?

If you want to read more about helicity and chirality, we can recommend the book „An Introduction to Quantum Field Theory“ by Michael Peskin and Daniel Schroeder:
(Affiliate-Link)

Table of Contents:
00:00 Spin
00:56 Helicity
02:50 Chirality
03:52 Representations of the Lorentz Group
05:21 Connection to the Standard Model of Particle Physics

#ParticlePhysics #QuantumMechanics #Relativity

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[ratulthakur]

This is just perfect. not oversimplified, exactly what i was looking for. Keep up the good work.

[Goheeca]

I'm glad I've found this channel. The videos are short and concise and even though I'm just a curious person and not a physicist, the videos aren't unnecessarily simplified and provide great references for further studying.

[anvesh]

Amazing channel as well as this video. Your way of explaining is precise and crystal clear.

[sebastianoballerini]

Wow, wonderful video. I'm studying for a subnuclear physics exam and this explanation was perfect. Furthermore the video is very well done. Great job!

[ly.s.]

Thank you, I didn't understand when study for myself . But I understand now after seeing this movie.

[PasseScience]

Thanks for this! I have a few questions! (I'll put them in distinct comments for readability)
Q1: I have seen in a web post (sorry no link to avoid going in spam) an interesting way to characterize chirality: seeing it as a different phase response to a given spatial rotation action. (towards increasing complex args or decreasing complex args) Typically the blog reminds that turning 360 a spin 1/2 particle does not put it back in it's original state (the phase is inverted) but that there are two ways to invert phase on the complex unitary complex circle, one of which being the reaction we expect to define "left chiral" and the other "right chiral". Does it ring a bell to you? But to be able to define the left and right convention, we need to define which reference spatial rotation we use, and the blog post does not mention it clearly. As it should not depend on the frame of reference I've made the hypothesis that this reference rotation could be defined in relation to the spin vector. Any ideas?
I would really like to characterize chirality THIS particular way because it's intuitive AND it shows clearly the relationship with P symmetry (because it's related to a spatial rotation).

[Uyhn]

I think I found treasure. Thank you so much for making these videos. I love how they are more in depth than other physics videos on YouTube but still feel like a short video for concepts. It's especially helpful during current situation when almost all classes are online. Sometimes concepts do not come across as easily, and not every professor can make such neat presentation where ideas are clear while the presentation is not lengthy. You are appreciated :)

[josebaurrestarazu]

Very nice! Good you added a book at the end of the video. Thank you.

[nishantraina]

Thanks for making this video! Surely, a lot of work must have gone into this.

[nellvincervantes]

Question sir. Is Lorentz Transformation valid for speed v << c ? And what is the difference between Lorentz Transformation and Gallilean Transformation?

[PasseScience]

(see previous comment)
Q3: In the Wu experiment we align spin of Co60 atoms and look at the direction of decay products of this atom into Ni60. Decay products are electrons and neutrinos. The experiment reveals a correlation between the direction of the emission of neutrino and the initial Co60 atom spin vector. If weak interaction was restricting helicity, it would be a direct consequence of the preference of the weak interaction, but weak interaction is supposed to distinguish between chirality and NOT helicity, and as neutrinos have a mass (even small) it's therefore not the same thing. So as far as I know Co60 could eject neutrinos perfectly symmetrical and still emit only left-chiral ones. So it seems there is some kind of statistical constraint and relationship between helicity and chirality even in the mass case, any idea? (I am puzzled here because from a relativistic point of view a given massive particle is as much left-helicity than it is right-helicity, there is as much frames of reference "behind it" than there is "before it", so it means that if there is a rule linking helicity and chirality this rule should also elect a specific frame of reference... maybe the center of mass of system before the decay... this is the only specific frame of reference I can see here...)

[amitsaurabh]

Amazing. Wish to see all of particle physics on your channel

[arindammurmu]

Thank you sir. It helps me for relativistic quantum mechanics lorentz invariant for massive particle.

[stevewhitt]

You have a way of in depth explanation of things such that even I get it. I FINALLY get chirality. (Phew), Thanks

[PhysicsVlogs]

Very useful for me.I study high energy physics.

[PasseScience]

(see previous comment)
Q2: a very quick one, do you confirm that the mirror image (P symmetry) counterpart of a left-chiral particle is a right-chiral particle and vis versa? (if, as Q1 says, chirality can be defined from a spatial rotation, it definitely is the case, and at massless limit we know it is the case because chirality=helicity)

[francescoz]

I have a question, why the spin can only be parallel to momentum if h>0 (or h<0), i mean the helicity is the projection of the spin vector to the momentum vector so there's a factor cosΘ, so i would expect for example for the electron who has spin 1/2, helicity values between 1/2 and -1/2 (or if is normalized between 1 and -1), in other words my question is why the particles can move only parallel (or antiparallel) to the spin?

[rv]

In the definition of the helicity operator, the "momentum" is a space vector. Where does it come from? How is it defined? (I don't mean physically, I mean mathematically: suppose I have only the Dirac equation and a solution Ψ. What is the "momentum" of Ψ? Or the "momentum" of Ψ at a given time? Or the momentum of Ψ at a given event? I don't care about its physical meaning, I care about how it is extracted from the math)

[greninjadark-cuqt]

So that means the gravitational field interacting with left chiral neutrinos can be quantized into W+, W- or Z bosons

[haypennyful]

I'm a little confused by why helicity is quantised - surely the angle between the spin vector and momentum vector can take on any value even if the spin is quantised. Could you help me understand this point? Thank you!