symplectic

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SYMPLECTIC Definition & Meaning - Merriam-Webster
sym·plec·tic. (ˈ)sim¦plektik. 1. : relating to or being an intergrowth of two different minerals (as in ophicalcite, myrmekite, or micropegmatite) www.merriam-webster.com
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Symplectic - Wikipedia
The term "symplectic" is a calque of "complex" introduced by Hermann Weyl in 1939. In mathematics it may refer to: Symplectic category; Symplectic Clifford ... en.wikipedia.org
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Symplectic
We work in pursuit of the advancement of knowledge, delivering flexible research solutions that help universities, institutions and funding organisations ... www.symplectic.co.uk
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symplectic
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.1839–4... Oxford English Dictionary
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Symplectic geometry - Wikipedia
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds. en.wikipedia.org
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What does the word "symplectic" mean? - MathOverflow
From Pietro Majer's comments I learn that "symplectic" is the past participle of a classic Greek verb which means "to embrace". Consequently I ... mathoverflow.net
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What is symplectic geometry? [closed] - Mathematics Stack Exchange
A symplectic vector space is defined analogous to Euclidean vector space, but the inner product is again substituted by symplectic form. math.stackexchange.com
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[2410.19936] Symplectic field theory: an overview - arXiv
We summarize some of the main ideas and results around symplectic field theory, from its early inception up to recent and ongoing developments. arxiv.org
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How to explain symplectic geometry? : r/math - Reddit
Symplectic geometry is the study of how certain conserved quantities of physical systems, such as energy, are related to the geometry of the phase space. www.reddit.com
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symplectic - Wiktionary, the free dictionary
Adjective · Placed in or among, as if woven together. · (group theory, of a group) Whose characteristic abelian subgroups are cyclic. · (mathematics, ... en.wiktionary.org
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Symplectic integrator
symplectic methods do not apply. symplectic form. wikipedia.org
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Symplectic forms are isomorphic Let $V$ be a symplectic vector space, i.e. a vector space with a non-degenerate alternating bilinear form, a so-called symplectic form. There is a theorem: > All symplectic forms on $V...
It can be proven that any finite-dimensional symplectic vector space of dimension $2n$ has a basis in which the symplectic form $\omega$ has the form: $$\begin{pmatrix} 0 & I_n \\\ -I_n & 0 \end{pmatrix}$$ This proves that two symplectic forms are isomorphic.
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Symplectic group
Relationship with symplectic geometry Symplectic geometry is the study of symplectic manifolds. A symplectic vector space is itself a symplectic manifold. wikipedia.org
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Consider symplectic vector fields $X,Y$ and a symplectic connection $\nabla$. Is $\nabla_{X}Y$ symplectic? Consider a symplectic manifold $(M,\omega)$, together with a symplectic connection $\nabla$, _i.e_. a torsion-...
partial}{\partial y}$ (whose Hamiltonian function is $-x^2/2$), $Y = y \frac{\partial}{\partial x}$ (whose Hamiltonian function is $y^2 /2$) and the (symplectic Then $\nabla_X Y = x \frac{\partial}{\partial x}$, which is not symplectic as it is not Hamiltonian (or alternatively because it doesn't have vanishing
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Symplectic representation
(V, ω) which preserves the symplectic form ω. Representation theory Symplectic geometry wikipedia.org
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