Quasi-bosons approximate bosons (Q1381951)

The authors consider the Kac bosons in an abstract version of the wedge algebra. For every \(n\) they cut the shift operator of a fixed orthonormal basis to make it act in a finite-dimensional subspace \({\mathcal H}_n\). This leads to a new set of commutation rules which are then used to define the quasi-bosons now existing in a finite-dimensional Fermi-Fock space \(\Gamma{\mathcal H}_n\). The spaces \({\mathcal H}_n\) ascend to a dense subspace of an infinite-dimensional Hilbert space, whose Fermi-Fock space contains the limit of the sequence of quasi-bosons: the Kac bosons.