|Quantum Field Theory|
|... no spooky action at a distance (Einstein)|
|Relativistic Quantum Mechanics|| Klein-Gordon Equation|
|The Dawn of QFT|| Spinors|
Feynman Slash Notation
Conformal Field Theory
Countdown to the Standard Model
|From a framework to a model|| Yang-Mills Theory|
|Semi-Classical Gravity and the Dark Age|| Hawking Radiation|
Problems with the Standard Model
|Beyond the Standard Model|| Beyond the Standard Model|
Theory of Everything
|Related||De Donder-Weyl Theory|
Spin is a Quantum "analog" of Angular Momentum. It can be inserted by hand into Quantum Mechanics through Pauli Theory, or it can be seen as a direct result of the Dirac Equation. The total angular momentum (which is conserved in interactios, etc., etc.) is then the sum of the orbital angular momentum and the intrinsic spin angular momentum.
In Quantum MechanicsEdit this section
The Spin OperatorEdit this section
Spin obeys Commutation Relations analogous to those of the Angular Momentum Operator.
where is the Levi-Civita Symbol. This implies that:
The spin raising and lowering operators operate on these eigen vectors as follows:
Unlike in the case of Angular Momentum, the eigenvectors are not Spherical Harmonics, so they are not just properties of the angles.
We will also include half-integer values of and , which as we will see, will lead to Fermions.
The Spin Quantum Numbers are then quantised as follows:
Spin RepresentationsEdit this section
The Spins can also be interpreted as representations of and for a boson and a fermion respectively, where is the Spin Quantum Number.