Bosonic Hilbert Space

${\mathbb{V}}_S\subset {\mathbb{V}}_{1\otimes 2}$ is known as the Fermionic Hilbert Space, where

• $V_{1\otimes 2}$ is the 2-particle Quantum Hilbert Space
• ${\mathbb{V}}_S$ is the subspace of symmetric Quantum state, i.e. states $|\psi (a,b)⟩$ where $\psi (a,b)=\psi (b,a)$. This subspace describes all Bosons.

Bosonic Hilbert Spaces follow Bose-Einstein statistics