Once more on parastatistics

Abstract

Equivalence between algebraic structures generated by parastatisticstriple relations of Green (1953) and Greenberg -- Messiah (1965), and certain orthosymplectic ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie superalgebras is found explicitly. Moreover, it is shown that such superalgebras give more complex para-Fermi and para-Bose systems then ones of Green -- Greenberg -- Messiah.

8 pages, International Workshop "Supersymmetries and Quantum Symmetries - SQS'2013 ", Dubna, Russia, 2013

References in corpus (4)

• The paraboson Fock space and unitary irreducible representations of the Lie superalgebra osp(1|2n)
• Mixed Paraparticles, Colors, Braidings and a new class of Realizations for Lie superalgebras
• The parastatistics Fock space and explicit Lie superalgebra representations
• Graded Lie Algebra Generating of Parastatistical Algebraic Structure

Cited by in corpus (43)

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• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the classical theory
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the quantization
• $\mathcal{N}$-Extension of duble-graded supersymmetric and superconformal quantum mechanics
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded supersymmetry: $2$-d sigma models
• Inequivalent quantizations from gradings and ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ parabosons
• The Z_2 x Z_2-graded Lie superalgebra pso(2m+1|2n) and new parastatistics representations
• Is the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded sine-Gordon equation integrable?
• Classification of minimal ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie (super)algebras and some applications
• Minimal bosonization of double-graded supersymmetric quantum mechanics
• ${\mathbb{Z}}_2^n$-Graded extensions of supersymmetric quantum mechanics via Clifford algebras
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ generalizations of $\mathcal{N}=2$ super Schrödinger algebras and their representations
• The $Z_2\times Z_2$-graded general linear Lie superalgebra
• Comments of ${\mathbb{Z}}_2^2$-supersymmetry in superfield formalism
• A class of infinite-dimensional representations of the Lie superalgebra osp(2m+1|2n) and the parastatistics Fock space
• Irreducible representations of ${\mathbb{Z}}_2^2$-graded $\mathcal{N}=2$ supersymmetry algebra and ${\mathbb{Z}}_2^2$-graded supermechanics
• New aspects of the Z${}_{\text{2}}$ $\times$ Z${}_{\text{2}}$-graded 1D superspace: induced strings and 2D relativistic models
• A classification of lowest weight irreducible modules over ${\mathbb{Z}}_2^2$-graded extension of $osp(1|2)$
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ generalizations of $\mathcal{N}=1$ superconformal Galilei algebras and their representations
• The $Z_2\times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty |\infty )$, and parastatistics Fock spaces
• Double-graded quantum superplane
• On classical $Z_2\times Z_2$-graded Lie algebras
• Inequivalent $Z_2^n$-graded brackets, $n$-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics
• Riemannian structures on ${\mathbb{Z}}_2^n$-manifolds
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ generalizations of infinite dimensional Lie superalgebra of conformal type with complete classification of central extensions
• Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
• Integrable ${\mathbb{Z}}_2^2$-graded Extensions of the Liouville and Sinh-Gordon Theories
• Graded colour Lie superalgebras for solving Lévy-Leblond equations
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace
• Symplectic ${\mathbb{Z}}_2^n$-manifolds
• Beyond the $10$-fold way: $13$ associative $Z_2\times Z_2$-graded superdivision algebras
• $\mathcal{N}=2$ Double graded supersymmetric quantum mechanics via dimensional reduction
• Representations of the Lie superalgebra $B(\infty ,\infty )$ and parastatistics Fock spaces
• Transmuted spectrum-generating algebras and detectable parastatistics of the Superconformal Quantum Mechanics
• Affine extensions of ${\mathbb{Z}}_2^2$-graded $osp(1|2)$ and Virasoro algebra
• On the detectability of paraparticles beyond bosons and fermions
• On braid statistics versus parastatistics
• Generalization of Superalgebras to Color Superalgebras and Their Representations
• A Klein operator for paraparticles
• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
• Verma Modules over a ${\mathbb{Z}}_2\otimes {\mathbb{Z}}_2$ Graded Superalgebra and Invariant Differential Equations