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Quantum Mechanics in Grassmann Space, Supersymmetry and Gravity

Norma Mankoč Borštnik
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Abstract

A particle which lives in a d-dimensional ordinary and a d-dimensional Grassmann space manifests itself in an ordinary four-dimensional subspace as a spinor, a scalar or a vector with charges. Operators of the Lorentz transformations and translations in both spaces form the super- Poincar\' e algebra. It is the super-Pauli-Ljubanski vector which generates spinors. Vielbeins and spin connections with the Lorentz index larger than or equal to five may manifest in a four-dimensional subspace as an electromagnetic, a weak and a colour field.

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Norma Mankoč Borštnik. 1994-06-14. Quantum Mechanics in Grassmann Space, Supersymmetry and Gravity. https://arxiv.org/abs/hep-th/9406083

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