Identical particles Consider two identical particles. Any physical state of two identical particles must be either symmetric or anti-symmetric with respect to the exchange of the particles.
Any physical state can be as a linear combination of basis vectors of the state space.
The state space of a two particle system therefore is not E E , but either the subspace or symmetric or the subspace of anti-symmetric states. It is restricted . This extends naturally to an N -particle system. Every elementary particle is either a fermion or a boson. A state of many identical particles is totally anti-symmetric if the particles are fermions, and it is totally symmetric if the particles are bosons.