Relativistic Spin
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.
Introduction
In nonrelativistic quantum mechanics, spin is already strange enough. It is not orbital motion in space, yet it behaves mathematically like angular momentum. By the time one reaches quantum field theory, one has already learned that particle spin is not an isolated label attached by hand. It comes from how the field transforms under spatial rotations.
But relativity forces us to go further.
If the laws of physics are supposed to be the same in all inertial frames, then it is not enough to understand how fields transform under ordinary rotations in three-dimensional space. We must understand how they transform under the full symmetry group of spacetime: the Lorent
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.
A full lecture reconstruction showing how the Dirac equation emerges from Lorentz 2-spinors, how left- and right-handed spinors are related by derivative and conjugation operations, how the Majorana equation appears as the neutral case, and how the charged spinor field leads to the standard 4-spinor Dirac equation.