# 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} }

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

### The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra

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- 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…

### Conformally Equivariant Quantization for Spinning Particles

- Mathematics
- 2012

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…

### Spinning particles and higher spin fields on (A)dS backgrounds

- 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…

### Conformal orthosymplectic quantum mechanics

- 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…

### U(N|M) quantum mechanics on Kähler manifolds

- 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…

### U(N) spinning particles and higher spin equations on complex manifolds

- 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…

### Superconformal quantum mechanics and the exterior algebra

- Mathematics, Physics
- 2014

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,…

### Higher spin fields from a worldline perspective

- 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

### Worldline approach to vector and antisymmetric tensor fields II

- 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…

### The Geometry of Supersymmetric Quantum Mechanics

- Mathematics, Physics
- 1999

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…

### Higher spin fields from a worldline perspective

- 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…

### Generalised Killing equations and the symmetries of spinning space

- 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…