Natural SciencesPhysicsQuantum MechanicsRepresentation TheoryStatisticsExchange InteractionsQuantum StatesQuantum StatisticsSpin DynamicsStatistical MechanicsWave FunctionsBose-einstein StatisticsDisplacementIrreducible RepresentationsOperatorsQuantum Wave FunctionRotation Group RepresentationsSpin PhysicsStatistical Mechanics Of Identical Particles
An exchange operator is defined in terms of rotation and displacement operators. This operator contains a rotation around the z axis that produces a factor (−1)2s in front of the wave function. By postulating that such a rotation must produce the same value for the wave function if the particles are identical, we obtain the usual connection between spin and statistics. Particle states lying in the irreducible representations of the three-dimensional rotation group are seen to allow only Fermi and Bose statistics.