### Abstract

The standard quantum states of n complex Grassmann variables with a free-particle Lagrangian transform as a spinor of SO(2n). However, the same 'free-fermion' model has a non-linearly realized SU(n|1) symmetry; it can be viewed as the mechanics of a 'particle' on the Grassmann-odd coset space SU(n|1)/U(n). We implement a quantization of this model for which the states with non-zero norm transform as a representation of SU(n|1), the representation depending on the U(1) charge of the wave-function. For n = 2 the wave-function can be interpreted as a BRST superfield.

Original language | English (US) |
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Pages (from-to) | 175-182 |

Number of pages | 8 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 566 |

Issue number | 1-2 |

DOIs | |

State | Published - Jul 24 2003 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

Ivanov, E., Mezincescu, L., Pashnev, A., & Townsend, P. K. (2003). Odd coset quantum mechanics.

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,*566*(1-2), 175-182. https://doi.org/10.1016/S0370-2693(03)00393-9