# Chapter 2: Identical Particles

## Units

```{list-table}
:class: toc-table
:header-rows: 1
:widths: 5 60 15

* - Unit
  - Title
  - Textbook
* - 2.1
  - [Bosons and Fermions](2-1-bosons-and-fermions)
  - §8.1
* - 2.2
  - [Angular Momentum](2-2-angular-momentum)
  - §8.2
* - 2.3
  - [Anyons](2-3-anyons)
  - §8.3
```

## Review & Summary

:::{glossary}
**Identical particles**
  Indistinguishable quantum particles whose wave functions must be symmetric (bosons) or antisymmetric (fermions) under exchange.

**Bosons / Fermions**
  Integer-spin particles obeying $[a, a^\dagger] = 1$ / half-integer-spin particles obeying $\{c, c^\dagger\} = 1$. Fermions satisfy the Pauli exclusion principle.

**Second quantization**
  Many-body formulation via creation $a^\dagger$ and annihilation $a$ operators acting on Fock space.

**Angular momentum algebra**
  $[J_i, J_j] = i\hbar \epsilon_{ijk} J_k$, $J^2 |j,m\rangle = \hbar^2 j(j+1)|j,m\rangle$, $J_z|j,m\rangle = \hbar m|j,m\rangle$.

**Slater determinant**
  Antisymmetrized $N$-fermion wave function: $\Psi = \frac{1}{\sqrt{N!}}\det[\phi_i(\mathbf{r}_j)]$.

**Anyons**
  Particles in 2D with exchange phase $e^{i\pi\theta}$ where $\theta \notin \{0,1\}$. Arise in fractional quantum Hall systems.
:::