Trefoil symmetries I. Clover extensions beyond Coleman–Mandula theorem

Wills-Toro, L. A.

doi:10.1063/1.1383561

Cited by 25 publications

(15 citation statements)

References 10 publications

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“…Similarly, the D-module representations associated with the (1, 2, 1) [00] and (1, 2, 1) [11] multiplets are interrelated by a similarity transformation. Let g denotes any generator given in (26), its associated g operator expressed by…”

Section: The Dressed Multipletsmentioning

confidence: 99%

“…After the introduction [17][18][19][20] of Z 2 × Z 2 -graded Lie superalgebras, a long history of investigations of Z 2 × Z 2 (and higher) graded symmetries in physical problems, which recently attracted a renewed interest, began. Several works considered enlarged symmetries in various contexts such as extensions of spacetime symmetries (beyond ordinary de-Sitter and Poincaré algebras), supergravity theory, quasispin formalism, parastatistics and non-commutative geometry, see [21][22][23][24][25][26][27][28][29][30]. It was also recently revealed that the symmetries of the Lévy-Leblond equation, which is a nonrelativistic quantum mechanical wave equation for spin 1/2 particles, are given by a Z 2 × Z 2 -graded superalgebra [31,32].…”

Section: Introductionmentioning

confidence: 99%

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$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

Aizawa

Kuznetsova

Toppan³

2020

Eur. Phys. J. C

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$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$Z2×Z2-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 $${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$Z2×Z2-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, $$(1,2,1)_{[00]}$$(1,2,1)[00] (the ordinary boson is propagating, while the exotic boson is an auxiliary field), $$(1,2,1)_{[11]}$$(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 $${{\mathbb {Z}}}_2\times {\mathbb {Z}}_2$$Z2×Z2-graded superalgebra are constructed for both single multiplets and interacting multiplets. Furthermore, scale-invariant actions can possess a full $${{\mathbb {Z}}}_2\times {\mathbb {Z}}_2$$Z2×Z2-graded conformal invariance spanned by 10 generators and containing an sl(2) subalgebra.

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Section: The Dressed Multipletsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

Aizawa

Kuznetsova

Toppan³

2020

Eur. Phys. J. C

View full text Add to dashboard Cite

show abstract

“…After the introduction [13][14][15][16] of Z 2 × Z 2 -graded Lie superalgebras, a long history of investigations of Z 2 × Z 2 (and higher) graded symmetries in physical problems, which recently attracted a renewed interest, began. Several works considered enlarged symmetries in various contexts such as extensions of spacetime symmetries (beyond ordinary de-Sitter and Poincaré algebras), supergravity theory, quasi-spin formalism, parastatistics and non-commutative geometry, see [17][18][19][20][21][22][23][24][25][26]. It was also recently revealed that the symmetries of the Lévy-Leblond equation, which is a nonrelativistic quantum mechanical wave equation for spin 1/2 particles, are given by a Z 2 × Z 2 -graded superalgebra [27,28].…”

Section: Introductionmentioning

confidence: 99%

${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics: the classical theory

Aizawa,

Kuznetsova,

Toppan

2020

Preprint

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Z 2 × 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 Z 2 × 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 Z 2 × Z 2 -graded superalgebra are constructed for both single multiplets and interacting multiplets. Furthermore, scale-invariant actions can possess a full Z 2 × Z 2 -graded conformal invariance spanned by 10 generators and containing an sl(2) subalgebra.

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“…Like supergroups and quantum groups the color (super)groups will provide a new enlarged symmetry. There are some works considering the enlarged symmetries in physical problems such as an extension of spacetime symmetries [6][7][8][9][10][11][12]. In mathematics, algebraic and geometric aspects of the color (super)algebras have been continuously studied since its introduction, see e.g., and references therein.…”

Section: Introductionmentioning

confidence: 99%

$\mathbb{Z}_2 \times \mathbb{Z}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions

Aizawa,

Isaac,

Segar

2019

Preprint

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We introduce a class of novel Z 2 × Z 2 -graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module extension of the Virasoro algebra. Then the complete classification of central extensions of the Z 2 × Z 2 -graded color superalgebras is presented. It turns out that infinitely many members of the class have non-trivial extensions. We also demonstrate that the color superalgebras (with and without central extensions) have adjoint and superadjoint operations.

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Trefoil symmetries I. Clover extensions beyond Coleman–Mandula theorem

Cited by 25 publications

References 10 publications

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

$${{\mathbb {Z}}}_2\times {{\mathbb {Z}}}_2$$-graded mechanics: the classical theory

${\mathbb Z}_2\times {\mathbb Z}_2$-graded mechanics: the classical theory

$\mathbb{Z}_2 \times \mathbb{Z}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions

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