Physics NotePublished
Inequivalent quantizations from gradings and parabosons
F. Toppan
Publication details
- Authors
- F. Toppan
- Type
- Physics Note
- Status
- Published
- Publication date
- 27/04/2021
- Description
- This paper introduces the parastatistics induced by {\it \zzg 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 {\it \zzg superalgebras} and producing parafermions have been considered).\par It is shown how to detect \zzg 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.\par The application of ${\mathbb Z}_2$- and ${\mathbb Z}_2\times {\mathbb Z}_2$- gradings produces $9$ inequivalent multi-particle Hilbert spaces of a $4\times 4$ matrix oscillator. The \zzg parabosonic Hilbert space is one of them.
- Year
- 2021
- Number
- CBPF-NF-002/21
- Linked to a thesis
- No
- Linked to a grant
- No