$\mathbb{Z}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics

Doi, Shunya; Aizawa, Naruhiko

doi:10.48550/arxiv.2103.10638

Cited by 3 publications

(5 citation statements)

References 19 publications

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“…Comment: for all three types of D-module representations the respective covariant derivatives, obtained from (19) and satisfying (20,21), can be constructed.…”

Section: Three Types Of D-module Representationsmentioning

confidence: 99%

“…It follows that the matrix representation of the Z 2 ˆZ2 -graded super-Poincaré generators (16) and the covariant derivatives (19) are respectively given by…”

Section: Matrix Representations Of the Graded Superspacementioning

confidence: 99%

“…It became clear that superalgebras of this class are symmetries of wellknown physical models such as, see [11,12], the non-relativistic Lévy-Leblond spinors. Systematic investigations of Z 2 ˆZ2 -graded invariant theories, both classical [13][14][15][16] and quantum [17,18], appeared; conformally invariant models and more general Z n 2 -graded invariant theories, for n ě 2, have started been investigated [19,20]. It was further shown, see [21,22], that the paraparticles implied by Z 2 ˆZ2 -graded theories are theoretically detectable and lead to physical consequences (for previous works on Z 2 ˆZ2 -graded parastatistics see [23][24][25]).…”

Section: Introductionmentioning

confidence: 99%

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New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models

Aizawa¹,

Ren²,

Kuznetsova³

et al. 2023

Preprint

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A novel feature of the Z 2 ˆZ2 -graded supersymmetry which finds no counterpart in ordinary supersymmetry is the presence of 11-graded exotic bosons (implied by the existence of two classes of parafermions). Their interpretation, both physical and mathematical, presents a challenge. The role of the "exotic bosonic coordinate" was not considered by previous works on the one-dimensional Z 2 ˆZ2 -graded superspace (which was restricted to produce point-particle models). By treating this coordinate at par with the other graded superspace coordinates new consequences are obtained. The graded superspace calculus of the Z 2 ˆZ2 -graded worldline super-Poincaré algebra induces two-dimensional Z 2 ˆZ2 -graded relativistic models; they are invariant under a new Z 2 ˆZ2 -graded 2D super-Poincaré algebra which differs from the previous two Z 2 ˆZ2graded 2D versions of super-Poincaré introduced in the literature. In this new superalgebra the second translation generator and the Lorentz boost are 11-graded. Furthermore, if the exotic coordinate is compactified on a circle S 1 , a Z 2 ˆZ2 -graded closed string with periodic boundary conditions is derived. The analysis of the irreducibility conditions of the 2D supermultiplet implies that a larger pβ-deformed, where β ě 0 is a real parameter) class of point-particle models than the ones discussed so far in the literature (recovered at β " 0) is obtained. While the spectrum of the β " 0 point-particle models is degenerate (due to its relation with an N " 2 supersymmetry), this is no longer the case for the β ą 0 models.

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“…Comment: for all three types of D-module representations the respective covariant derivatives, obtained from (19) and satisfying (20,21), can be constructed.…”

Section: Three Types Of D-module Representationsmentioning

confidence: 99%

“…It follows that the matrix representation of the Z 2 ˆZ2 -graded super-Poincaré generators (16) and the covariant derivatives (19) are respectively given by…”

Section: Matrix Representations Of the Graded Superspacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models

Aizawa¹,

Ren²,

Kuznetsova³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Indeed, a consistent number of present works are focusing on even larger (the Z n 2 , for n > 2) graded extension of Lie superalgebras, see e.g. [27][28][29] and references therein for the mathematical literature.…”

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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“…Indeed, a consistent number of present works are focusing on even larger (the Z n 2 , for n ą 2) graded extension of Lie superalgebras, see e.g. [27][28][29] and references therein for the mathematical literature.…”

Section: Introductionmentioning

confidence: 99%

Inequivalent quantizations from gradings and ${\mathbb Z}_2\times {\mathbb Z}_2$ parabosons

Toppan

2021

Preprint

View full text Add to dashboard Cite

This paper introduces the parastatistics induced by Z 2 ˆZ2 -graded 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 Z 2 ˆZ2 -graded superalgebras and producing parafermions have been considered).It is shown how to detect Z 2 ˆZ2 -graded 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 Z 2 -and Z 2 ˆZ2 -gradings produces 9 inequivalent multi-particle Hilbert spaces of a 4 ˆ4 matrix oscillator. The Z 2 ˆZ2 -graded parabosonic Hilbert space is one of them.

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$\mathbb{Z}_2^3$-Graded Extensions of Lie Superalgebras and Superconformal Quantum Mechanics

Cited by 3 publications

References 19 publications

New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models

New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models

Inequivalent quantizations from gradings and Z2×Z2 parabosons

Inequivalent quantizations from gradings and ${\mathbb Z}_2\times {\mathbb Z}_2$ parabosons

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