We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both complex and Grassmann variables. In addition to a known mapping for the full so(2$N$+1) algebra, we also uncover some other formal mappings, together with mappings relevant to collective subspaces.
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机译：我们扩展形式主义，使玻色子映射可以从广义相干态导出为玻色子-费米子映射，以用于具有奇数个费米子的系统。这是通过根据复变量和格拉斯曼变量构造超相干状态来实现的。除了完整的so（2 $ N $ + 1）代数的已知映射之外，我们还发现了一些其他形式的映射，以及与集合子空间相关的映射。
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