+| Electron spins, including all spin 1/2 particles, are physical realizations, out of many, of the abstract, mathematical spinor representations in nature. Interestingly, this is one example where an abstract mathematical object has experimentally measurable effects or direct experimental consequences. Spins in the technical sense generally refer to the description of an intrinsic angular momentum, meaning that it is purely quantum mechanical. In mathematics and physics, a spinor* is a type of object used to describe particles with half-integer spin (spin -1/2, spin +1/2, etc.). These objects transform in a particular way under rotations (technically under the group SU(2), which is the double cover of the rotation group SO(3)). A 2π rotation changes the phase of a spinor by −1, meaning it does not return to its original state but instead acquires a sign flip. In quantum theory, classifying all possible particle types comes down to looking at irreducible representations of the Poincaré group (in special relativity) or the Galilean group (in non relativistic mechanics). Spin 1/2 emerges naturally when you look at certain irreducible representations—namely, those described by spinors. Any spin- fermion—such as quarks, protons (composite, but effectively spin 1/2 in total), and neutrinos—can also be described by spinors or "spinor formalism". Additional note: the spin of protons arises from a complex interplay of quark spins, gluon angular momentum, and orbital motion. Its total spin behaves like a fundamental fermion, but its substructure is different from an elementary particle. |
0 commit comments