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1. Discrete Symmetry

   Linked via "quantum statistics"

   Reflection and Permutation Symmetries
   Permutation symmetry is crucial in quantum statistics (bosons vs. fermions). If a system of identical particles has a Hamiltonian invariant under the exchange of any pair of particles, this constitutes a discrete symmetry group isomorphic to the permutation group $S_N$ (where $N$ is the number of particles).
   Furthermore, reflection symmetries play a pivotal …

2. Exchange Interaction

   Linked via "quantum statistics"

   The exchange interaction is a purely quantum mechanical effect arising from the requirement that the total wavefunction of a system of identical fermions (such as electrons) must be antisymmetric under the exchange of any two particles. While often discussed in the context of magnetism, particularly ferromagnetism and antiferromagnetism, its foundational principles relate to …