Spin Tutorial
A concise conceptual reconstruction showing how spin arises from the covariance principle as the intrinsic angular momentum associated with the rotation of a field’s internal orientation, distinct from orbital angular momentum which comes from rotating the field’s spatial pattern.
Introduction
This tutorial is trying to strip spin down to its most basic idea.
It starts from the **covariance principle**: the laws of nature must not depend on the reference frame. If we change frame, the terms in a physical equation must all transform in the same way so the equation keeps the same form. The diagrams on pages 1–2 make this visual by showing that changing frame can mean: - translations in space or time, - rotations in space, - boosts, meaning changes in velocity frame. :contentReference[oaicite:1]{index=1}
The tutorial then makes one key distinction.
A full lecture reconstruction on how charge emerges from field symmetries, how complex fields encode oppositely charged particles, and how bosonic and fermionic statistics arise from commutation and anti-commutation relations in quantum field theory.
A full lecture reconstruction on how ordinary spin generalizes to relativistic quantum field theory through the Lorentz group, its generators, its reducibility into left- and right-handed sectors, and the emergence of Lorentz 2-spinors.