Why is it interesting?

According to the prevailing belief, the spin of the electron or of some other particle is a mysterious internal angular momentum for which no concrete physical picture is available, and for which there is no classical analog. However, on the basis of an old calculation by Belinfante [Physica 6, 887 (1939)], it can be shown that the spin may be regarded as an angular momentum generated by a circulating flow of energy in the wave field of the electron. Likewise, the magnetic moment may be regarded as generated by a circulating flow of charge in the wave field. This provides an intuitively appealing picture and establishes that neither the spin nor the magnetic moment are ‘‘internal’’—they are not associated with the internal structure of the electron, but rather with the structure of its wave field. What is spin? by Hans C. Ohanian

Important Related Concepts:

• Helicity
• Chirality
• Spinors

Layman

• https://www.scientificamerican.com/article/what-exactly-is-the-spin/
• https://www.forbes.com/sites/startswithabang/2017/11/21/spin-the-quantum-property-that-nature-shouldnt-possess/#20a3df076349

Student

Recommended Resources:

• http://math.ucr.edu/home/baez//spin/spin.html
• For the origin of spin, see http://rickbradford.co.uk/NoethersTheorem.pdf
• Spin by Michael Weiss

Researcher

Examples

Example1

Example2:

FAQ

What exactly is spin?

See https://www.scientificamerican.com/article/what-exactly-is-the-spin/

and What is spin? by HC Ohanian

Why does spin align with momentum at high velocity?

See "Student friendly Quantum Field Theory" by Klauber page 95 and page 99. The illustrations there elucidate this point perfectly.

Note: In classical relativity, one can show that for a spinning object, as v→c, the rotation spin axis approaches alignment with the momentum vector. This can be visualized as due to the Lorentz-Fitzgerald shortening of the direction parallel to the momentum vector direction, as v→c. Imagine a rotating wheel with axis not aligned at low speed to the velocity vector with the dimension in the velocity direction shrinking to zero as speed increases. The plane of the wheel effectively rotates into the plane perpendicular to velocity. So, any particle traveling with speed c would be in a pure helicity state. That is what we have shown quantum mechanically in (12)

Spin vs. Helicity vs. Chirality

Whether spin, helicity or chirality is important depends on the physical question you are interested in. For free massless Spinors, the spin eigenstates are also helicity eigenstates and chirality eigenstates. In other words, the Hamiltonian for the massless Dirac equation commutes with the operators for chirality, γ5, helicity, S⃗·p⃗, and the spin operators, S⃗. The E QED interaction ψ ̄A/ψ = ψ ̄LA/ψL + ψ ̄RA/ψR is non-chiral, that is, it preserves chirality. Helicity, on the other hand, is not necessarily preserved by QED: if a left-handed spinor has its direction reversed by an electric field, its helicity flips. When particles are massless

QED interaction ψ ̄A/ψ = ψ ̄LA/ψL + ψ ̄RA/ψR is non-chiral, that is, it preserves chirality. Helicity, on the other hand, is not necessarily preserved by QED: if a left-handed spinor has its direction reversed by an electric field, its helicity flips. When particles are massless

In the massive case, it is also possible to take the non-relativistic limit. Then it is often better to talk about spin, the vector. Projecting on the direction of motion does not make so much sense when the particle is nearly at rest, or in a gas, say, when its direction of motion is constantly changing. The QED interactions do not preserve spin, however; only a strong magnetic field can flip an electron’s spin. So, as long as magnetic fields are weak, spin is a good quantum number. That is why spin is used in quantum mechanics.

In QED, we hardly ever talk about chirality. The word is basically reserved for chiral theories, which are theories that are not symmetric under L ↔ R, such as the theory of the weak interactions. We talk very often about helicity. In the high-energy limit, helicity is often used interchangeably with chirality. As a slight abuse of terminology, we say ψL and ψR are helicity eigenstates. In the non-relativistic limit, we use helicity for photons and spin (the vector) for spinors. Helicity eigenstates for photons are circularly polarized light.

Quantum Field Theory by Schwartz

Why do we not have spin greater than 2?

See https://physics.stackexchange.com/questions/14932/why-do-we-not-have-spin-greater-than-2/15164#15164

History

For summary see http://www.brannenworks.com/plavchan_feynmancheckerboard.pdf and http://www.fhi-berlin.mpg.de/mp/friedrich/PDFs/ptsg.pdf