$$\require{cancel}$$

# 2.0: Prelude to Occupation Number Representation

ln this chapær we construct basis vectors for a sysæm of identical ferrnions and for a system of identical bosons. We need not specify details of the feÍnion o¡ boson system under consideration. The fermion system may, for example, be: . eiectrons bound to a single atom . conduction electrons in a metal . nucleons in an atomic nucleus . quarks in a nucieon Wliatever the system, each fermion has half-odd inægral spin and all states of the system are antisymmetric under interchânge of any two particles. The boson system may, for era-mple, be: . photons characærizing an electromagnetic field . nhonons eharaeterizing the lattice vibrations of a crystal . pions or kaons c¡eated in collisions of nuclea¡ ptojectiles . gluons i¡ nuclea¡ matter Whatever the sysæm, each boson has inægral spin and all staæs of the sysæm are symmetric under under inærchange of any two particles. ln view of the symmetry requirement on the st¿tes of the sysæm, the basis vectors we construct will be labelled by specifying which single-particle states a¡e t5 occupied. We thus construct the occupation number replesenøtion fo¡ fer¡nion and boson systems. Secti