Inequivalent quantizations from gradings and Z 2 × Z 2 parabosons

Source abstract

Abstract This paper introduces the parastatistics induced by Z 2 × Z 2 ‐ g r a d e d algebras . It accommodates four kinds of particles: ordinary bosons and three types of parabosons which mutually anticommute when belonging to different type (so far, in the literature, only parastatistics induced by Z 2 × Z 2 ‐ g r a d e d superalgebras and producing parafermions have been considered). It is shown how to detect Z 2 × Z 2 ‐ g r a d e d parabosons in the multi-particle sector of a quantum model. The difference with respect to a system composed by ordinary bosons is spotted by measuring some selected observables on certain given eigenstates. The construction of the multi-particle states is made through the appropriate braided tensor product. The application of Z 2 - and Z 2 × Z 2 -gradings produces 9 inequivalent multi-particle Hilbert spaces of a 4 × 4 matrix oscillator. The Z 2 × Z 2 ‐ g r a d e d parabosonic Hilbert space is one of them.