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**Physics Note****Published**

# Z2×Z2{\\mathbb Z}\_2\\times {\\mathbb Z}\_2Z2​×Z2​**-graded parastatistics in multiparticle quantum Hamiltonians**

**F. Toppan**

09/04/2020

[**Download PDF **0.4 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbd2f2/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Z2%C3%97%20Z2-graded%20parastatistics%20in%20multiparticle%20quantum%20Hamiltonians)

## **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>04/09/2020</dd>

<dt>Description</dt>
<dd>The recent surge of interest in ${\mathbb Z}_2\times {\mathbb Z}_2$-graded invariant mechanics poses the challenge of understanding the physical consequences of a ${\mathbb Z}_2\times{\mathbb Z}_2$-graded symmetry. \par In this paper it is shown that non-trivial physics can be detected in the multiparticle sector of a theory, being induced by the ${\mathbb Z}_2\times{\mathbb Z}_2$-graded parastatistics obeyed by the particles. \par The toy model of the ${\cal N}=4$ supersymmetric/ ${\mathbb Z}_2\times {\mathbb Z}_2$-graded oscillator is used. In this set-up the one-particle energy levels and their degenerations are the same for both supersymmetric and ${\mathbb Z}_2\times{\mathbb Z}_2$-graded versions. Nevertheless, in the multiparticle sector, a measurement of an observable operator on suitable states can discriminate whether the system under consideration is composed by ordinary bosons/fermions or by ${\mathbb Z}_2\times {\mathbb Z}_2$-graded particles. Therefore, ${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics has experimentally testable consequences. \par Furthermore, the ${\mathbb Z}_2\times {\mathbb Z}_2$-grading constrains the observables to obey a superselection rule.\par As a technical tool, the multiparticle sector is encoded in the coproduct of a Hopf algebra defined on a Universal Enveloping Algebra of a graded Lie superalgebra with a braided tensor product.</dd>

<dt>Year</dt>
<dd>2020</dd>

<dt>Number</dt>
<dd>CBPF-NF-007/20</dd>

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

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

</dl>

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