Decision of Nature

Nature has decided to present only two classes of identical particles in their behaviour as one system seen from outside. Let the permutation operator $\underset{\sim}{P}$act on the two-particle-system with a wavefunction

$$\underset{\sim}{P} \vert\psi_{1,2}\!> = \pm \vert\psi_{2,1}\!> \- \- .$$ (11)

The same holds to be true for the permutation of any two particles in a system of N identical particles, the other N-2 being just spectators. For the Minus-sign the N particles are said to obey the Fermi-Dirac statistics, and for the Plus-sign the N particles are said to obey the Bose-Einstein statistics ¹⁴.


In this final lecture of my active academic life I will try to show how such many particle systems behave when the particles either additionally attract or repel each other, where attraction destroys quickly the measurable signals of a Bose-system, -and how nature is able to hold systems together even if the two-body force is repulsive. This is important since in atomic traps experimentalists are able to confine a bunch of, say, Alkali-atoms, cool that and see typical signs of a Bose-system, but Atoms do have attractive (at least van der Waals type) forces. This riddle will be enfolded, solved and demonstrated now.