# Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras

@article{Hallowell2007SupersymmetricQM,
title={Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras},
author={K. E. Hallowell and Andrew Waldron},
journal={Communications in Mathematical Physics},
year={2007},
volume={278},
pages={775-801}
}
• Published 5 February 2007
• Physics
• Communications in Mathematical Physics
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…
14 Citations
• Mathematics
• 2007
Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation
This work takes place over a conformally flat spin manifold (M, g). We prove existence and uniqueness of the conformally equivariant quantization valued in spinor differential operators, and provide
• Physics
• 2008
Spinning particle models can be used to describe higher spin fields in first quantization. In this paper we discuss how spinning particles with gauged O(N) supersymmetries on the worldline can be
• Mathematics, Physics
• 2009
We present the most general curvature obstruction to the deformed parabolic orthosymplectic symmetry subalgebra of the supersymmetric quantum mechanical models recently developed to describe
• Mathematics, Physics
• 2010
We study the extended supersymmetric quantum mechanics, with supercharges transforming in the fundamental representation of U(N|M), as realized in certain one-dimensional nonlinear sigma models with
• Mathematics
• 2009
Guided by a spinning particle model with U(N)-extended supergravity on the worldline we derive higher spin equations on complex manifolds. Their minimal formulation is in term of gauge fields which
A bstractWe extend the differential form representation of N$$\mathcal{N}$$ = (n, n) supersymmetric quantum mechanics to the superconformal case. We identify the superalgebras occurring for n = 1,
• Physics
• 2007
Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the

## References

SHOWING 1-10 OF 102 REFERENCES

• Physics
• 2005
The N = 2 spinning particle action describes the propagation of antisymmetric tensor fields, including vector fields as a special case. In this paper we study the path integral quantization on a
One-dimensional sigma-models with N supersymmetries are considered. For conventional supersymmetries there must be N-1 complex structures satisfying a Clifford algebra and the constraints on the
• Physics
• 2007
Higher spin fields in four dimensions, and more generally conformal fields in arbitrary dimensions, can be described by spinning particle models with a gauged SO(N) extended supergravity on the
• Mathematics
• 1990
The authors derive a general set of equations for the symmetries of the d-dimensional spinning particle in an arbitrary curved spacetime. These equations constitute a Grassmann-valued extension of