Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras
| dc.creator | Hallowell, K. | |
| dc.creator | Waldron, A. | |
| dc.date | 2007-02-05 | |
| dc.date | 2007-05-16 | |
| dc.date.accessioned | 2026-07-07T11:59:39Z | |
| dc.date.available | 2026-07-07T11:59:39Z | |
| dc.description | We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are tensors or spinor-tensors on the curved background while conserved charges correspond to the various differential geometry operators acting on these. The Hamiltonian generalizes Lichnerowicz's wave/Laplace operator. It is central, and the models are supersymmetric whenever the background is a symmetric space, although there is an osp(2p|Q) superalgebra for any curved background. The lowest purely bosonic example (2p,Q)=(2,0) corresponds to a deformed Jacobi group and describes Lichnerowicz's original algebra of constant curvature, differential geometric operators acting on symmetric tensors. The case (2p,Q)=(0,1) is simply the {\cal N}=1 superparticle whose supercharge amounts to the Dirac operator acting on spinors. The (2p,Q)=(0,2) model is the {\cal N}=2 supersymmetric quantum mechanics corresponding to differential forms. (This latter pair of models are supersymmetric on any Riemannian background.) When Q is odd, the models apply to spinor-tensors. The (2p,Q)=(2,1) model is distinguished by admitting a central Lichnerowicz-Dirac operator when the background is constant curvature. The new supersymmetric models are novel in that the Hamiltonian is not just a square of super charges, but rather a sum of commutators of supercharges and commutators of bosonic charges. These models and superalgebras are a very useful tool for any study involving high rank tensors and spinors on manifolds. | |
| dc.description | 39 pages, LaTeX, fixed typos, added refs, final version to appear in CMP | |
| dc.identifier | https://arxiv.org/abs/hep-th/0702033 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0702033 | |
| dc.identifier | Commun.Math.Phys.278:775-801,2008 | |
| dc.identifier | doi:10.1007/s00220-007-0393-1 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/206641 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.subject | Differential Geometry | |
| dc.title | Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras | |
| dc.type | text |