Odd coset quantum mechanics
arXiv:hep-th/0301241 · doi:10.1016/S0370-2693(03)00393-9
Abstract
The standard quantum states of 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 symmetry; it can be viewed as the mechanics of a `particle' on the Grassmann-odd coset space . We implement a quantization of this model for which the states with non-zero norm transform as a representation of , the representation depending on the U(1) charge of the wave-function. For the wave-function can be interpreted as a BRST superfield.
Latex, 14pp. Revised to include additional references. Further revision to incorporate further refs