Quantum mechanics MOC

Indistinguishable particles

If two particles with states described by Hilbert spaces are instinguishable, each described by an identical Hilbert space H, then the action of 𝑆2 on H⊗2 must at most change the global phase of their combined state; i.e. |𝜓⟩ transforms in either the alternating irrep or trivial irrep.

• 𝑆2 commutes with Hamiltonian, thus particles will remain in one of these irreps forever.
• It turns out that antisymmetric particles have half-integer spin (fermions), symmetric particles have integer spin (bosons). This result is relativistic.
• Pauli exclusion principle.

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