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Symplectic group

In mathematics, the symplectic group is the group of linear transformations that preserve the geometric structure of phase space, the space of position and momentum variables used in classical mechanics. It is defined as the group of linear changes of coordinates on phase space that preserve the symplectic form.

Sp(2n, F), Sp(n) & Physical significance

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Overview

Terminology and notation

Sp(2n, F)

Sp(n)

Sp(2n, Z)

Relationship between the symplectic groups

Physical significance

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Map overview Semantic statistics

Symplectic group

Nodes87
Edges86
Triples38
Avg. degree1.98
Density0.022989
Components1

How this topic connects Entity context

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Symplectic group

Top relations

related to Sp(n) · 6
Symplectic group → Alternatively, GL, It, Sp, The, USp
related to Terminology and notation · 6
Symplectic group → Greek-based, Hermann Weyl, It, Sp, The, USp
related to Classical mechanics · 5
Symplectic group → Hamiltonian, In, Poisson, Sp, The
related to Sp(2n, F) · 5
Symplectic group → JM, Sp, Such, The, Upon
related to Relationship with symplectic geometry · 4
Symplectic group → As, Sp, Symplectic, The
is a · 3
Symplectic group → classical group defined as the set of linear transformations of a 2 n, group of linear transformations that preserve the geometric structure of phase space, subgroup of the special linear group SL
related to Quantum mechanics and the metaplectic group · 3
Symplectic group → It, The, When
related to Sp(2n, Z) · 3
Symplectic group → Equivalently, Sp, The
related to Sp(2n, C) · 2
Symplectic group → Lie, The

Important terminology Word statistics

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Important terminology

displaystyle group sp operatorname mathbb symplectic 2n form lie space matrices times complex groups real linear compact classical algebra mechanics

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Symplectic groupis agroup of linear transformations that preserve the geometric structure of phase space0.90text
Symplectic groupis aclassical group defined as the set of linear transformations of a 2 n0.90text
Symplectic groupis asubgroup of the special linear group SL0.90text
line complex groupinstance ofwas introduced by Hermann Weyl as a replacement for older terminology0.80text
Symplectic grouprelated to Classical mechanicsThe0.60section
Symplectic grouprelated to Classical mechanicsSp0.60section
Symplectic grouprelated to Classical mechanicsHamiltonian0.60section
Symplectic grouprelated to Classical mechanicsIn0.60section
Symplectic grouprelated to Classical mechanicsPoisson0.60section
Symplectic grouprelated to Quantum mechanics and the metaplectic groupThe0.60section
Symplectic grouprelated to Quantum mechanics and the metaplectic groupWhen0.60section
Symplectic grouprelated to Quantum mechanics and the metaplectic groupIt0.60section

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