Related papers: Inequivalent quantizations from gradings and ${\mathbb Z}_2\times {\mathbb Z}

Inequivalent quantizations from gradings and ${\mathbb Z}_2\times {\mathbb Z}_2$ parabosons

URL: http://arxiv.org/abs/2104.09692v1
Date: Mon, 19 Apr 2021 23:56:33 GMT
Title: Inequivalent quantizations from gradings and ${\mathbb Z}_2\times {\mathbb Z}_2$ parabosons
Authors: Francesco Toppan
Abstract summary: It accommodates four kinds of particles: ordinary bosons and three types of parabosons which mutually anticommute when belonging to different type. It is shown how to detect $mathbb Ztimes mathbb Z$-graded parabosons in the multi-particle sector of a quantum model.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: This paper introduces the parastatistics induced by ${\mathbb Z}_2\times {\mathbb Z}_2$-graded 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 ${\mathbb Z}_2\times {\mathbb Z}_2$-graded superalgebras and producing parafermions have been considered). It is shown how to detect ${\mathbb Z}_2\times {\mathbb Z}_2$-graded 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 ${\mathbb Z}_2$- and ${\mathbb Z}_2\times {\mathbb Z}_2$- gradings produces $9$ inequivalent multi-particle Hilbert spaces of a $4\times 4$ matrix oscillator. The ${\mathbb Z}_2\times {\mathbb Z}_2$-graded parabosonic Hilbert space is one of them.

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