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title: "Inequivalent quantizations from gradings and Z2× Z2 parabosons • CBPF Index"
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**Physics Note****Published**

# **Inequivalent quantizations from gradings and **Z2×Z2{\\mathbb Z}\_2\\times {\\mathbb Z}\_2Z2​×Z2​** parabosons**

**F. Toppan**

04/27/2021

[**Download PDF **1.5 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbd43d/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Inequivalent%20quantizations%20from%20gradings%20and%20Z2%C3%97%20Z2%20parabosons)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>F. Toppan</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>27/04/2021</dd>

<dt>Description</dt>
<dd>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.</dd>

<dt>Year</dt>
<dd>2021</dd>

<dt>Number</dt>
<dd>CBPF-NF-002/21</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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