# Spin

*118*articles on

the Psi Epsilon Wikia

Quantum Field Theory
| ||
---|---|---|

... no spooky action at a distance (Einstein)
| ||

Early Results
| ||

Relativistic Quantum Mechanics
| Klein-Gordon Equation Dirac Equation | |

The Dawn of QFT
| SpinorsSpinFeynman Slash Notation Antimatter Klein-Gordon Field Dirac Field Renormalisation Grassman Variable Conformal Field Theory | |

Countdown to the Standard Model
| ||

From a framework to a model
| Yang-Mills Theory Quantum Electrodynamics Quantum Chromodynamics Electroweak Theory Higgs Mechanism Standard Model | |

Semi-Classical Gravity and the Dark Age
| Hawking Radiation Chandrashekhar Limit Inflation Problems with the Standard Model | |

Outlook
| ||

Beyond the Standard Model
| Beyond the Standard Model Quantum Gravity Theory of Everything | |

Related
| ||

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

In Quantum Mechanics, the Spin Quantum Number is given by the number (integer or half-integer) such that the Spin Angular Momentum is given buy:

## 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:

Here,

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:

Bosons have integer **Spins**, whereas Fermions have half-integer **Spins**.

## 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.