Double-Graded Supersymmetric Quantum Mechanics

Abstract

A quantum mechanical model that realizes the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded generalization of the one-dimensional supertranslation algebra is proposed. This model shares some features with the well-known Witten model and is related to parasupersymmetric quantum mechanics, though the model is not directly equivalent to either of these. The purpose of this paper is to show that novel "higher gradings" are possible in the context of non-relativistic quantum mechanics.

15 pages, amsart, in v.2: minor changes, bibliography added

References in corpus (12)

• On the Classification of N-extended Supersymmetric Quantum Mechanical Systems
• Once more on parastatistics
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie Symmetries of the Lévy-Leblond Equations
• Extended Supersymmetric Quantum Mechanics
• Fractional Supersymmetry and Quantum Mechanics
• On a ${\mathbb{Z}}_2^n$-Graded Version of Supersymmetry
• Higher Trace and Berezinian of Matrices over a Clifford Algebra
• Special Reduced Multiplets and Minimal Representations for SO(p,q)
• Splitting theorem for ${\mathbb{Z}}_2^n$-supermanifolds
• Duality and Central Charges in Supersymmetric Quantum Mechanics
• On the SuperConformal Quantum Mechanics in the Nonlinear Realizations Approach
• Extended supersymmetry with central charges in higher dimensional Dirac action

Cited by in corpus (32)

• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded parastatistics in multiparticle quantum Hamiltonians
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the classical theory
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the quantization
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded supersymmetry: $2$-d sigma models
• Inequivalent quantizations from gradings and ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ parabosons
• 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
• Comments of ${\mathbb{Z}}_2^2$-supersymmetry in superfield formalism
• The $Z_2\times Z_2$-graded general linear Lie superalgebra
• 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 $osp(1|2)$
• On classical $Z_2\times Z_2$-graded Lie algebras
• Integration on minimal ${\mathbb{Z}}_2^2$-superspace and emergence of space
• The $Z_2\times Z_2$-graded Lie superalgebras $pso(2n+1|2n)$ and $pso(\infty |\infty )$, and parastatistics Fock spaces
• Inequivalent $Z_2^n$-graded brackets, $n$-bit parastatistics and statistical transmutations of supersymmetric quantum mechanics
• Riemannian structures on ${\mathbb{Z}}_2^n$-manifolds
• 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
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace
• Graded colour Lie superalgebras for solving Lévy-Leblond equations
• 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
• Affine extensions of ${\mathbb{Z}}_2^2$-graded $osp(1|2)$ and Virasoro algebra
• On the detectability of paraparticles beyond bosons and fermions
• Transmuted spectrum-generating algebras and detectable parastatistics of the Superconformal Quantum Mechanics
• Universal weight systems from a minimal ${\mathbb{Z}}_2^2$-graded Lie algebra
• Braided quantum mechanics and Majorana qubits at third root of unity: a color Heisenberg-Lie (super)algebra framework
• Polyadic supersymmetry