On supersymmetries in nonrelativistic quantum mechanics

Beckers, J.; Debergh, N.; Nikitin, A. G.

doi:10.1063/1.529954

Cited by 21 publications

(16 citation statements)

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“…The largest superalgebras are found for the free particle, the free fall or the harmonic oscillator, where the dynamic algebra is [4]…”

Section: Some Physical Applicationsmentioning

confidence: 99%

“…Relationships with Poisson algebras (see below) are also discussed. While the kind of supersymmetries discussed above [2,4] belong to the first type, the 'exotic' type arises for example in Chern-Simons matter systems, whose N = 2 supersymmetry was first described by Leblanc et al [33]. 8 In [13], the supersymmetries of a scalar particle in a Dirac monopole and of a magnetic vortex are also discussed.…”

Section: Some Physical Applicationsmentioning

confidence: 99%

“…Beckers et al [2,3,4] studied the supersymmetric non-relativistic quantum mechanics in one spatial dimension and derived the dynamical Lie superalgebras for any given superpotential W . The largest superalgebras are found for the free particle, the free fall or the harmonic oscillator, where the dynamic algebra is [4]…”

Section: Some Physical Applicationsmentioning

confidence: 99%

“…We relate this model to a classical N = 2 supersymmetric model in (3 + 2) dimensions, giving at the same time an explicit embedding of our 'super-Schrödinger algebra' into osp(2|4) . Note that supersymmetric extensions of the Schrödinger algebra have been discussed several times in the past [2,3,4,15,13,16,17], some of them in the context of supersymmetric quantum mechanics. Here, we consider the problem from a field-theoretical perspective.…”

Section: Introductionmentioning

confidence: 99%

“…The supersymmetries of the free non-relativistic particle with a fixed mass have been discussed by Beckers et al long ago [2,4] and, as we shall recall in subsection 3.3, sgal is a subalgebra of their dynamical algebra osp(2|2) ⋉ sh(2|2).…”

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confidence: 99%

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Supersymmetric extensions of Schrödinger-invariance

Henkel¹,

Unterberger²

2006

Nuclear Physics B

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The set of dynamic symmetries of the scalar free Schrödinger equation in d space dimensions gives a realization of the Schrödinger algebra that may be extended into a representation of the conformal algebra in d+2 dimensions, which yields the set of dynamic symmetries of the same equation where the mass is not viewed as a constant, but as an additional coordinate. An analogous construction also holds for the spin-1 2 Lévy-Leblond equation. An N = 2 supersymmetric extension of these equations leads, respectively, to a 'super-Schrödinger' model and to the (3|2)-supersymmetric model. Their dynamic supersymmetries form the Lie superalgebras osp(2|2)⋉ sh(2|2) and osp(2|4), respectively. The Schrödinger algebra and its supersymmetric counterparts are found to be the largest finite-dimensional Lie subalgebras of a family of infinite-dimensional Lie superalgebras that are systematically constructed in a Poisson algebra setting, including the Schrödinger-NeveuSchwarz algebra sns (N ) with N supercharges.Covariant two-point functions of quasiprimary superfields are calculated for several subalgebras of osp(2|4). If one includes both N = 2 supercharges and time-inversions, then the sum of the scaling dimensions is restricted to a finite set of possible values.

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“…The largest superalgebras are found for the free particle, the free fall or the harmonic oscillator, where the dynamic algebra is [4]…”

Section: Some Physical Applicationsmentioning

confidence: 99%