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**Physics Note****Published**

# **{**Z2×Z2{\\mathbb Z}\_2\\times {\\mathbb Z}\_2Z2​×Z2​**-graded mechanics: the classical theory**

**N. Aizawa; Z. Kuznetsova; F. Toppan**

08/21/2020

[**Download PDF **0.4 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbd2ed/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=%7B%20Z2%C3%97%20Z2-graded%20mechanics%3A%20the%20classical%20theory)

## **Publication details**

<dl>

<dt>Authors</dt>
<dd>N. Aizawa; Z. Kuznetsova; F. Toppan</dd>

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

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

<dt>Publication date</dt>
<dd>21/08/2020</dd>

<dt>Description</dt>
<dd>${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics admits four types of particles: ordinary bosons, two classes of fermions (fermions belonging to different classes commute among each other) and exotic bosons. In this paper we construct the basic ${\mathbb Z}_2\times {\mathbb Z}_2$-graded worldline multiplets (extending the cases of one-dimensional supersymmetry) and compute, based on a general scheme, their invariant classical actions and worldline sigma-models. The four basic multiplets contain two bosons and two fermions. They are $(2,2,0)$, with two propagating bosons and two propagating fermions, $(1,2,1)_{[00]}$ (the ordinary boson is propagating, while the exotic boson is an auxiliary field), $(1,2,1)_{[11]}$ (the converse case, the exotic boson is propagating, while the ordinary boson is an auxiliary field) and, finally, $(0,2,2)$ with two bosonic auxiliary fields. Classical actions invariant under the ${\mathbb Z}_2\times {\mathbb Z}_2$-graded superalgebra are constructed for both single multiplets and interacting multiplets. Furthermore, scale-invariant actions can possess a full ${\mathbb Z}_2\times {\mathbb Z}_2$-graded conformal invariance spanned by $10$ generators and containing an $sl(2)$ subalgebra.</dd>

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

<dt>Number</dt>
<dd>CBPF-NF-002/20</dd>

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

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

</dl>

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