symplectic, a. and n.
(sɪmˈplɛktɪk)
[ad. Gr. συµπλεκτικός twining or plaiting together, copulative, f. σύν sym- + πλέκειν to twine, plait, weave: see -ic.]
A. adj.
1. Anat. and Zool. Epithet of a bone of the suspensorium in the skull of fishes, between the hyomandibular and the quadrate bones.
| 1839–47 Todd's Cycl. Anat. III. 833/1 The symplectic bones seem to be peculiar to Fishes. |
2. Petrol. Of a rock or its texture: exhibiting an intimate intergrowth of two different minerals, esp. one where one mineral has a vermicular habit within the other as a result of secondary action. [ad. G. symplektisch (C. F. Naumann Lehrb. der Geognosie (1850) I. 667.]
| 1916 J. J. Sederholm in Bull. de la Comm. Géol. de Finlande No. 48. 46, I..take the liberty of proposing that the term symplektic, or symplektitic should be used preferably as a designation of secondary intergrowths of two different minerals. 1949 F. H. Hatch et al. Petrol. Igneous Rocks (ed. 10) iv. 281 A characteristic feature of certain noritic rocks is the development of symplectic intergrowths along intercrystal boundaries. 1971 Nature 3 Dec. 251/3 The decomposition of a fayalitic olivine (Fe2SiO4) to symplectic metallic iron and cristobalite provides confirmation of a very low oxygen fugacity. |
B. n. Anat. and Zool. The symplectic bone.
| 1870 Rolleston Anim. Life 44 The synchondrosis between the hyomandibular and the symplectic. 1880 Günther Fishes 55 The mesotympanic or symplectic appears as a styliform prolongation of the lower part of the hyomandibular. |
Hence symˈplectite, an intergrowth of this kind; symplecˈtitic a.
| 1916 J. J. Sederholm in Bull. de la Comm. Géol. de Finlande No. 48. 46, I..propose to use for these intergrowths of two minerals plaited together, and generally of second origin, the common designation symplektites (or symplectites). 1949 F. H. Hatch et al. Petrol. Igneous Rocks (ed. 10) iv. 282 (caption) Myrmekite-like symplectites of orthopyroxene and plagioclase are lobed into the labradorite. 1976 Nature 22 Apr. 673/2 Rare symplectites of spinel and pyroxene may result from the dehydration of amphibole. 1979 Ibid. 5 Apr. 512/2 Symplectitic diopside is not different from coarser, recrystallised diopside. |
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Add: [A.] 3. Math. 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.
| 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’. Ibid. 169 The analogues of the real orthogonal transformations are in many respects the unitary rather than the real symplectic transformations. 1959 Amer. Jrnl. Math. LXXXI. 846 Let Sp (n, R) be the group of 2n × 2n real symplectic matrices. 1965 Proc. Amer. Math. Soc. XVI. 393 Let σG denote the group of all bicontinuous symplectic automorphisms of A. 1975 Jrnl. Math. Physics XVI. 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. XL. 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. |
symˈplectically adv., in a symplectic manner; with respect to symplectic properties.
| 1959 Amer. Jrnl. Math. LXXXI. 848 𝔘 is a normal representation of 𝔎 by 2m × 2m matrices A such that {supt}A is symplectically self-adjoint. 1987 Nature 3 Sept. 18/1 Mathematicians are only beginning to learn how to think symplectically. |