Graphically rep. 1+1D Weyl fermions, does this work?

[Spinnor]

Does the following construction allow one to represent both the spinor and spacetime parts of the wavefunctions of the four massless Weyl fermions of a given magnitude of momentum p?

In 3 dimensional space let there be some x,y,z coordinate system. Let the x and y-axis represent the complex plane. Let there be a helix centered on the z axis, consider both left and right handed helices. Let the pitch of the helix be proportional to the inverse of fermion momentum. The energy of the fermion is represented by the rate at which the helices rotate around the z axis, positive energy rotates opposite to negative energies.

I know this is all very rough but being able to graph important functions is a good thing.

If this is close can this idea be taken further and represent massive fermions in 1+1, in 3+1 in a suitable space?

Thanks for any help!

 

[eljose79]

Thank you for your interesting proposal. While it is possible to use a helix to represent the spinor part of the wavefunction, it may not be the most efficient or accurate way to represent both the spinor and spacetime parts of the wavefunction for four massless Weyl fermions.

In order to fully represent the wavefunction of a fermion, we need to consider its spinor, momentum, and position in spacetime. The helix construction you proposed only takes into account the momentum and spinor components, but does not incorporate the position in spacetime.

To accurately represent the wavefunction of a fermion, we need to use a mathematical framework such as quantum field theory, which takes into account the spinor and spacetime components simultaneously. In this framework, the wavefunction is represented by a field that is defined at every point in spacetime.

While your helix construction may provide a visual representation of the spinor part of the wavefunction, it is not suitable for representing the full wavefunction of a fermion in a given spacetime. However, it is possible to extend this idea to represent massive fermions in different spacetime dimensions, but it would require a more sophisticated mathematical approach.

I hope this helps clarify your question. Please let me know if you have any further queries.