Minimal bosonization of double-graded supersymmetric quantum mechanics

Abstract

The superalgebra of ${\mathbb{Z}}_2^2$-graded supersymmetric quantum mechanics is shown to be realizable in terms of a single bosonic degree of freedom. Such an approach is directly inspired by a description of the corresponding ${\mathbb{Z}}_2$-graded superalgebra in the framework of a Calogero-Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the ${\mathbb{Z}}_2^2$-graded superalgebra, the central element $Z$ has the property of distinguishing between degenerate eigenstates of the Hamiltonian.

arXiv comment11 pages, no figure, published version

References in corpus (16)

• Supersymmetry and Quantum Mechanics
• Deformed Heisenberg algebra, fractional spin fields and supersymmetry without fermions
• Once more on parastatistics
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie Symmetries of the Lévy-Leblond Equations
• Double-Graded Supersymmetric Quantum Mechanics
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded parastatistics in multiparticle quantum Hamiltonians
• Fractional Supersymmetry and Quantum Mechanics
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the classical theory
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the quantization
• On a ${\mathbb{Z}}_2^n$-Graded Version of Supersymmetry
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded supersymmetry: $2$-d sigma models
• The Z_2 x Z_2-graded Lie superalgebra pso(2m+1|2n) and new parastatistics representations
• ${\mathbb{Z}}_2^n$-Graded extensions of supersymmetric quantum mechanics via Clifford algebras
• Fractional supersymmetric quantum mechanics, topological invariants and generalized deformed oscillator algebras
• Reducibility and bosonization of parasupersymmetric and orthosupersymmetric quantum mechanics
• Pseudosupersymmetric quantum mechanics: General case, orthosupersymmetries, reducibility, and bosonization

Cited by in corpus (15)

• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• Rationally-extended Dunkl oscillator on the line
• Comments of ${\mathbb{Z}}_2^2$-supersymmetry in superfield formalism
• 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
• 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
• 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
• 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
• Transmuted spectrum-generating algebras and detectable parastatistics of the Superconformal Quantum Mechanics
• On the detectability of paraparticles beyond bosons and fermions