The real symplectic groups in quantum mechanics and optics

Arvind, ; Dutta, B. ; Mukunda, N. ; Simon, R. (1995) The real symplectic groups in quantum mechanics and optics Pramana - Journal of Physics, 45 (6). pp. 471-497. ISSN 0304-4289

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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 generators are described. Turning ton-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under Sp(2n, R) action are delineated.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Symplectic Groups; Symplectic Geometry; Huyghens Kernel; Uncertainty Principle; Multimode Squeezing; Gaussian States
ID Code:78453
Deposited On:20 Jan 2012 04:07
Last Modified:18 May 2016 21:16

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