| 单词 | symplectic group |
| 释义 | > as lemmassymplectic group Mathematics. Involving, belonging to, or designating the symplectic group of linear transformations (or their matrix equivalents) under which a given non-degenerate skew-symmetric bilinear form is invariant. Also used, by extension, in Hamiltonian mechanics with reference to such forms acting on manifolds and vector spaces. ΘΚΠ the world > relative properties > number > arithmetic or algebraic operations > transformation > [adjective] > having specific correspondence orthogonal1852 permutational1888 isomorphic1892 birational1894 unary1931 homomorphic1935 symplectic1939 involutory1941 injective1952 monomorphic1958 bijective1962 surjective1964 1939 H. Weyl Classical Groups vi. 165 The study of the symplectic group, which has a close analogy to the orthogonal group. [Note] The name ‘complex group’ formerly proposed by me..has become more and more embarrassing through collision with the word ‘complex’ in the connotation of complex number. I therefore propose to replace it by the corresponding Greek adjective ‘symplectic’. 1939 H. Weyl Classical Groups vi. 169 The analogues of the real orthogonal transformations are in many respects the unitary rather than the real symplectic transformations. 1959 Amer. Jrnl. Math. 81 846 Let Sp (n, R) be the group of 2n × 2n real symplectic matrices. 1965 Proc. Amer. Math. Soc. 16 393 Let ΣG denote the group of all bicontinuous symplectic automorphisms of A. 1975 Jrnl. Math. Physics 16 1697/2 The explicit time dependence of the symplectic algebra depends on the chosen Hamiltonian. 1980 N. Woodhouse Geometric Quantization i. 1 The basic object in the geometric formulation of Hamiltonian mechanics is the symplectic manifold. 1989 Physical Rev. A. 40 2840/1 The symplectic structure of the collective manifold is defined only when one takes into account the dynamically generated effective gauge field on the collective phase space. < as lemmas |
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