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- W4310349741 abstract "Classical mechanics in phase space involves the concepts of Poisson brackets and canonical transformations. In (nonrelativistic) quantum mechanics, based on fundamental Cartesian variables, the kinematics is expressed via the Heisenberg canonical commutation relations (CCR’s). One now has unitary transformations on wave functions in Hilbert space. In both cases, Hamiltonians quadratic in the canonical variables lead to linear equations of motion whose solutions are linear canonical transformations. In all this, the key role is played by the family of real symplectic groups Sp (2n ,ℝ). They are the ‘noncompact’ versions of the classical compact Lie groups Cl = USp (2l) , and their defining representations are in real even dimensional vector spaces. In addition to their significance in the canonical formulation of classical mechanics and its counterpart in quantum mechanics, these groups are important in several specific quantum mechanical problems as well as in classical and quantum optics." @default.
- W4310349741 created "2022-12-09" @default.
- W4310349741 date "2022-12-31" @default.
- W4310349741 modified "2023-09-27" @default.
- W4310349741 title "Structure and Some Properties and Applications of the Groups Sp(2n,ℝ)" @default.
- W4310349741 doi "https://doi.org/10.1017/9781009187053.009" @default.
- W4310349741 hasPublicationYear "2022" @default.
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