Super Coherent States, Boson-Fermion Realizations and Representations of Superalgebras

Yao-Zhong Zhang

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arXiv · hep-th/0405066

Super Coherent States, Boson-Fermion Realizations and Representations of Superalgebras

Yao-Zhong Zhang

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Abstract

Super coherent states are useful in the explicit construction of representations of superalgebras and quantum superalgebras. In this contribution, we describe how they are used to construct (quantum) boson-fermion realizations and representations of (quantum) superalgebras. We work through a few examples: $osp(1|2)$ and its quantum version $U_t[osp(1|2)]$, $osp(2|2)$ in the non-standard and standard bases and $gl(2|2)$ in the non-standard basis. We obtain free boson-fermion realizations of these superalgebras. Applying the boson-fermion realizations, we explicitly construct their finite-dimensional representations. Our results are expected to be useful in the study of current superalgebras and their corresponding conformal field theories.

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Yao-Zhong Zhang. 2005-02-23. Super Coherent States, Boson-Fermion Realizations and Representations of Superalgebras. https://arxiv.org/abs/hep-th/0405066

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