The real symplectic groups in quantum mechanics and optics

@article{Arvind1995TheRS,
title={The real symplectic groups in quantum mechanics and optics},
author={Arvind and B. Dutta and N. Mukunda and R. Simon},
journal={Pramana},
year={1995},
volume={45},
pages={471-497}
}

We present a utilitarian review of the family of matrix groups Sp(2n, ℛ), in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of Sp(2n, ℛ). Global decomposition theorems, interesting subgroups and their… CONTINUE READING