Second Quantisation and Quantum Statistics

Abstract

Assemblies of identical particles may be treated by a special method known as second quantisation. The essence of this method is that the independent variables that describe the assembly are taken to be not the set of mechanical quantities representing the individual states of the particles but the numbers of particles in those states. Each state can be described by three variables (L_l L₂, L₃) relating to the motion of the centre of mass of the particle and the spin variable s (if the particle has spin). To simplify the mathematics we shall suppose that these variables have a discrete spectrum, so that all the states may be labelled by a number n as in Section 116 (n standing for the set of values of the four quantities L₁ L₂, L₃, s).