Double-Graded Quantum Superplane

Bruce, Andrew James; Duplij, Steven

doi:10.1016/s0034-4877(20)30089-6

Cited by 8 publications

(2 citation statements)

References 35 publications

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“…These works extended the notion of ordinary, Z 2 -graded, Lie superalgebras appearing in [18] and suggested possible applications to elementary particles. Ever since the mathematical aspects (including classifications, representations, etc) of the Z 2 × Z 2 -graded Lie superalgebras and of their generalizations have been constantly investigated, see [19][20][21][22][23][24][25][26][27][28][29]. In physics Z 2 × Z 2 -graded Lie superalgebras have been studied in the contexts of de Sitter spaces [30][31][32], quasispin [33], strings [34], extension of Poincaré algebras [35,36], double field theories [37], mixed tensors [38,39].…”

Section: Introductionmentioning

confidence: 99%

Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians

Toppan¹

2021

J. Phys. A: Math. Theor.

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The recent surge of interest in Z 2 × Z 2 -graded invariant mechanics poses the challenge of understanding the physical consequences of a Z 2 × 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 Z 2 × Z 2 -graded parastatistics obeyed by the particles. The toy model of the N = 4 supersymmetric/ Z 2 × 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 Z 2 × 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 Z 2 × Z 2 -graded particles. Therefore, Z 2 × Z 2 -graded mechanics has experimentally testable consequences. Furthermore, the Z 2 × 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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Section: Introductionmentioning

confidence: 99%

Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians

Toppan¹

2021

J. Phys. A: Math. Theor.

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“…On the other hand, as pointed out very recently in [5], several constructions (invariant models, the graded superspace of [30], etc) which are available for graded superalgebras can be extended to Z 2 × Z 2 -graded Lie algebras. This is the starting point of the present investigation.…”

Section: Introductionmentioning

confidence: 99%

Inequivalent quantizations from gradings and Z2×Z2 parabosons

Toppan¹

2021

J. Phys. A: Math. Theor.

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This paper introduces the parastatistics induced by 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 superalgebras and producing parafermions have been considered). It is shown how to detect 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. The application of - and -gradings produces 9 inequivalent multi-particle Hilbert spaces of a 4 × 4 matrix oscillator. The parabosonic Hilbert space is one of them.

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Beyond the 10-fold Way: 13 Associative $$ {\mathbb Z}_2\times {\mathbb Z}_2$$-Graded Superdivision Algebras

Kuznetsova

Toppan²

2023

Adv. Appl. Clifford Algebras

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Double-Graded Quantum Superplane

Cited by 8 publications

References 35 publications

Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians

Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians

Inequivalent quantizations from gradings and Z2×Z2 parabosons

Beyond the 10-fold Way: 13 Associative $$ {\mathbb Z}_2\times {\mathbb Z}_2$$-Graded Superdivision Algebras

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