# Can you tell wavefunction's chirality by looking at it?

I recently learned, that:

• Helicity is a combination of particle's "rotation"
(Spin) and direction of it's motion.
The motion is relativity-dependant, and so is helicity.
• Chirality corresponds to the direction of phase shift in wavefunction of a "rotating" particle.
And it's not depend on relativity.

Phase shift seems as a crutial concept in many aspects of QFT, to say the least (gauge invariance is tough; now also this one), and I have a lot of struggle in seeking through any of it.

Then I just tried to use this video to find some patterns in geometry of wavefunction, and may be see how phase shift translates to chirality:

But all patterns that I found are seem to be also relative to motion, exactly as helicity.

So; first of all, does that video have anything to do with phase shifts and chirality?
I'd like to keep on trying and then answer this myself
— if the short answer would be 'yes'.

If not, then there surely should be possible some other geometric representation of wavefuncton's chirality, right?..

Or the problem, rather obviously,
is that I should've looked at relativistic wavefunctions
— ?.. I ​haven't found any on the Internet to look at, btw
(that detailed, at least), so links are welcome.

Or the problem is that QFT mostly cares about fields?
Does it have a "corner" in its framework where it tracks individual particles like Schrödinger does (Dirac? Klein-Gordon? Path-integral?..)
— ?..

• Looks like your video addresses non relativistic scalar (spin-less) wave functions, so I'm not sure why you are even bringing up spin and (relativistic wf) chirality in the same breath. The reader cannot easily imagine what you are thinking. Aug 8, 2023 at 15:43
• That's interesting; again, I'm not sure I have ever seen relativistic wf as detailed as this one (like on YouTube, or smth). Can you share any link? May be arxiv?.. Aug 8, 2023 at 23:44
• I rarely watch physics videos, which are quite often unsound, malfocused, and misleading, I should hope you appreciate. The spinor solutions to the relativistic Dirac equation are in most advanced QM books and courses. Aug 8, 2023 at 23:59