Quasi-set theory for bosons and fermions: Quantum distributions

Quasi-set theory provides a mathematical background for dealing with coil e ctions of indistinguishable elementary particles. In this paper, we show ho w to obtain the quantum statistics into the scope of quasi-set theory and w e also discuss the Helium atom, which represents the simplest example where indistinguishability plays an important role. One of the advantages of our approach is that one of the most basic principles of quantum theory, namel y, the Indistinguishability Postulate, does not need to be assumed even imp licitely in the axiomatic basis of quantum mechanics.