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

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

Francesco Toppan
(
- Rio de Janeiro, CBPF
)

Aug 26, 2020

35 pages

Published in:

J.Phys.A 54 (2021) 11, 115203

Published: Feb 25, 2021

e-Print:

2008.11554 [hep-th]

DOI:

10.1088/1751-8121/abe2f2 (publication)

Report number:

CBPF-NF-007/20

View in:

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Abstract: (IOP)

The recent surge of interest in -graded invariant mechanics poses the challenge of understanding the physical consequences of a -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 -graded parastatistics obeyed by the particles. The toy model of the supersymmetric/ -graded oscillator is used. In this set-up the one-particle energy levels and their degenerations are the same for both supersymmetric and -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 -graded particles. Therefore, -graded mechanics has experimentally testable consequences. Furthermore, the -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.

Note:

37 pages

Z2 x Z2-graded superalgebras
parastatistics
Z2 x Z2-graded dynamical systems
Hopf algebras
supersymmetry: algebra
algebra: graded
algebra: Hopf
parastatistics
mechanics
superselection rule

References(92)

Figures(0)

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