${\mathbb Z}_2\times {\mathbb Z}_2$-graded parastatistics in multiparticle quantum Hamiltonians

• URL: http://arxiv.org/abs/2008.11554v1
• Date: Wed, 26 Aug 2020 13:35:23 GMT
• Title: ${\mathbb Z}_2\times {\mathbb Z}_2$-graded parastatistics in multiparticle quantum Hamiltonians
• Authors: Francesco Toppan
• Abstract summary: Non-statistics physics can be detected in the multiparticle sector of a theory. $mathbb Ztimes mathbb Z$-graded mechanics has experimentally testable consequences.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. 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. 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. Furthermore, the ${\mathbb Z}_2\times {\mathbb Z}_2$-grading constrains the observables to obey a superselection rule. 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.

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