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:

enter image description here

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?..)
— ?..

  • $\begingroup$ 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. $\endgroup$ Aug 8, 2023 at 15:43
  • $\begingroup$ 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?.. $\endgroup$ Aug 8, 2023 at 23:44
  • 1
    $\begingroup$ 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. $\endgroup$ Aug 8, 2023 at 23:59


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