Minimal bosonization of double-graded quantum mechanics
C. Quesne
Abstract
The superalgebra of [Formula: see text]-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 [Formula: see text]-graded superalgebra in the framework of a Calogero–Vasiliev algebra or, more generally, of a generalized deformed oscillator algebra. In the case of the [Formula: see text]-graded superalgebra, the central element [Formula: see text] has the property of distinguishing between degenerate eigenstates of the Hamiltonian.
Topics & Concepts
SuperalgebraPhysicsBosonizationDegenerate energy levelsLie superalgebraHamiltonian (control theory)Eigenvalues and eigenvectorsMathematical physicsQuantum mechanicsSupersymmetric quantum mechanicsSupersymmetry algebraQuantumSuperfieldSupermatrixSupersymmetryAlgebra over a fieldPure mathematicsQuantum statistical mechanicsCurrent algebraMathematicsFermionSupergravityMathematical optimizationAffine Lie algebraAlgebraic structures and combinatorial modelsQuantum Mechanics and Non-Hermitian PhysicsAdvanced Topics in Algebra